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[]\OT1/phv/m/n/10 GUAVA \OT1/ptm/m/n/10 is re-leased un-der the GNU Gen-eral Pu
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\OT1/phv/m/n/10 GUAVA\OT1/ptm/m/n/10 , though as doc-u-men-ta-tion it is re-lea
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\OT1/ptm/m/n/10 Cur-rently known bugs and sug-gested \OT1/phv/m/n/10 GUAVA \OT1
/ptm/m/n/10 projects are listed on the bugs and projects web page
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Chapter 1.
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Chapter 2.

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\OT1/ptm/m/n/10.95 This is also called the (Ham-ming) dis-tance be-tween $\OML/
ptmcm/m/it/10.95 v \OT1/ptmcm/m/n/10.95 = (\OML/ptmcm/m/it/10.95 v[]; :::; v[]\
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Chapter 3.
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Chapter 4.
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[]\OT1/ptm/m/n/10.95 The re-sult re-turned is a record with two fields; the fir
st, \OT1/pcr/m/n/10.95 mindist\OT1/ptm/m/n/10.95 , gives the low-est
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\OT1/ptm/m/n/10.95 rectly, so the com-mand was only found af-ter read-ing all t
he \OT1/ptm/m/it/10.95 *.gi \OT1/ptm/m/n/10.95 files in the \OT1/phv/m/n/10.95 
GUAVA \OT1/ptm/m/n/10.95 li-
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[]\OT1/ptm/m/n/10.95 For long codes, this method is faster in prac-tice than th
e in-ter-po-la-tion method used in
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[]\OT1/ptm/m/n/10.95 This uses \OT1/pcr/m/n/10.95 AutomorphismGroup \OT1/ptm/m/
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[57]
Chapter 5.

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[]\OT1/ptm/m/n/10.95 The four forms this com-mand can take are \OT1/pcr/m/n/10.
95 HadamardCode(H,t)\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 HadamardCode(H)\OT1
/ptm/m/n/10.95 ,
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[]\OT1/ptm/m/n/10.95 The func-tion \OT1/pcr/m/n/10.95 RandomLinearCode \OT1/ptm
/m/n/10.95 re-turns a ran-dom lin-ear code (see \OT1/pcr/m/n/10.95 RandomLinear
Code
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[]\OT1/ptm/m/n/10.95 The next func-tions we de-scribe gen-er-ate some well-know
n codes, like Ham-ming codes
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! Missing $ inserted.
<inserted text> 
                $
l.3309 ... b\ |\ a, b in K, a \not= 0 \}$. Here a^
                                                  H denotes the orbit of a u...
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you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
<inserted text> 
                $
l.3316 
       
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[]\OT1/ptm/m/n/10.95 A group K to-gether with a group of au-to-mor-phism H of K
 such that the semidi-
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\OT1/ptm/m/n/10.95 rect prod-uct KH is a Frobe-nius group with com-ple-ment H i
s called a Fer-rero pair (K,
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\OT1/ptm/m/n/10.95 H) in SONATA. Take a Frobe-nius (G,+) group with ker-nel K a
nd com-ple-ment H. Con-
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\OT1/ptm/m/n/10.95 sider the de-sign D with point set K and block set $\OMS/pzc
cm/m/n/10.95 f\OML/ptmcm/m/it/10.95 a[] \OT1/ptmcm/m/n/10.95 + \OML/ptmcm/m/it/
10.95 b \OMS/pzccm/m/n/10.95 j \OML/ptmcm/m/it/10.95 a; binK; a \OMS/pzccm/m/n/
10.95 6\OT1/ptmcm/m/n/10.95 = 0\OMS/pzccm/m/n/10.95 g$\OT1/ptm/m/n/10.95 . Here

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\OT1/ptm/m/n/10.95 a$[]\OML/ptmcm/m/it/10.95 denotestheorbitofaunderconjugation
byelementsofH:Everyplanarnear \OMS/pzccm/m/n/10.95 ^^@ \OML/ptmcm/m/it/10.95 ri
ngdesignoftype\OT1/ptmcm/m/n/10.95 " \OMS/pzccm/m/n/10.95 ^^C
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\OT1/ptmcm/m/n/10.95 "\OML/ptmcm/m/it/10.95 canbeobtainedinthiswayfromgroups:Th
esedesigns\OT1/ptmcm/m/n/10.95 (\OML/ptmcm/m/it/10.95 fromaFrobeniuskerneloford
ervandaFrobeniuscomplementoforderk\OT1/ptmcm/m/n/10.95 )\OML/ptmcm/m/it/10.95 h
avev \OMS/pzccm/m/n/10.95 ^^C
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\OT1/ptmcm/m/n/10.95 (\OML/ptmcm/m/it/10.95 v \OMS/pzccm/m/n/10.95 ^^@ \OT1/ptm
cm/m/n/10.95 1)\OML/ptmcm/m/it/10.95 =kdistinctblocksandtheyareallofsizek:Moreo
vereachofthevpointsoccursinexactlyv \OMS/pzccm/m/n/10.95 ^^@
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\OT1/ptmcm/m/n/10.95 1\OML/ptmcm/m/it/10.95 distinctblocks:Hencetherowsandtheco
lumnsoftheincidencematrixMofthedesignarealwaysofconstantweight:$ 
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! Missing $ inserted.
<inserted text> 
                $
l.3323 means that for all q = p^
                                k in P, OrderMod( p, m ) must divide q (see the
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
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                $
l.3325 
       
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\OT1/ptm/m/n/10.95 p$[]\OML/ptmcm/m/it/10.95 inP; OrderMod\OT1/ptmcm/m/n/10.95 
(\OML/ptmcm/m/it/10.95 p; m\OT1/ptmcm/m/n/10.95 )\OML/ptmcm/m/it/10.95 mustdivi
deq\OT1/ptmcm/m/n/10.95 (\OML/ptmcm/m/it/10.95 seetheSONATAdocumentationforFpfA
utomorphismGroupsCyclic\OT1/ptmcm/m/n/10.95 )\OML/ptmcm/m/it/10.95 :$ 
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[]\OT1/ptm/m/n/10.95 Finally we de-scribe the triv-ial codes (see \OT1/pcr/m/n/
10.95 WholeSpaceCode \OT1/ptm/m/n/10.95 ([][]5.5.10[][]), \OT1/pcr/m/n/10.95 Nu
llCode \OT1/ptm/m/n/10.95 ([][]5.5.11[][]),
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\OT1/pcr/m/n/10.95 RepetitionCode \OT1/ptm/m/n/10.95 ([][]5.5.12[][])), and the
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lic codes
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[]\OT1/ptm/m/n/10.95 This com-mand re-turns a "record" ob-ject \OT1/pcr/m/n/10.
95 C \OT1/ptm/m/n/10.95 with sev-eral ex-tra com-po-nents (type
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[]\OT1/ptm/m/n/10.95 This com-mand re-turns a "record" ob-ject \OT1/pcr/m/n/10.
95 C \OT1/ptm/m/n/10.95 with sev-eral ex-tra com-po-nents (type
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\OT1/pcr/m/n/10.95 NamesOfComponents(C) \OT1/ptm/m/n/10.95 to see them all): \O
T1/pcr/m/n/10.95 C!.points \OT1/ptm/m/n/10.95 (namely []), \OT1/pcr/m/n/10.95 C
!.degree \OT1/ptm/m/n/10.95 (namely []),
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[]\OT1/ptm/m/n/10.95 The weighted ver-sion has im-ple-mented with the op-tion
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[]\OT1/ptm/m/n/10.95 This com-mand re-turns a "record" ob-ject \OT1/pcr/m/n/10.
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[]\OT1/ptm/m/n/10.95 This com-mand re-turns a "record" ob-ject \OT1/pcr/m/n/10.
95 C \OT1/ptm/m/n/10.95 with sev-eral ex-tra com-po-nents (type
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[95]
Chapter 6.

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\OT1/ptm/m/n/10.95 ([][]6.1.6[][]), \OT1/pcr/m/n/10.95 RemovedElementsCode \OT1
/ptm/m/n/10.95 ([][]6.1.7[][]), \OT1/pcr/m/n/10.95 AddedElementsCode \OT1/ptm/m
/n/10.95 ([][]6.1.8[][]), \OT1/pcr/m/n/10.95 ShortenedCode \OT1/ptm/m/n/10.95 (
[][]6.1.9[][]),
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\OT1/pcr/m/n/10.95 LengthenedCode \OT1/ptm/m/n/10.95 ([][]6.1.10[][]), \OT1/pcr
/m/n/10.95 ResidueCode \OT1/ptm/m/n/10.95 ([][]6.1.11[][]), \OT1/pcr/m/n/10.95 
ConstructionBCode \OT1/ptm/m/n/10.95 ([][]6.1.12[][]), \OT1/pcr/m/n/10.95 DualC
ode
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\OT1/ptm/m/n/10.95 To undo ex-tend-ing, call \OT1/pcr/m/n/10.95 PuncturedCode \
OT1/ptm/m/n/10.95 (see \OT1/pcr/m/n/10.95 PuncturedCode \OT1/ptm/m/n/10.95 ([][
]6.1.2[][])). The func-tion
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[109] [110]
Chapter 7.

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[]\OT1/ptm/m/n/10.95 Firstly, we de-scribe func-tions that com-pute spe-cific u
p-per bounds on the code size
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[]\OT1/ptm/m/n/10.95 The re-sult-ing record can be used in the func-tion \OT1/p
cr/m/n/10.95 BestKnownLinearCode \OT1/ptm/m/n/10.95 (see
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[]\OT1/ptm/m/n/10.95 If the cov-er-ing ra-dius of [] is known, a list of length
 1 is re-turned.
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\OT1/pcr/m/n/10.95 BoundsCoveringRadius \OT1/ptm/m/n/10.95 makes use of the fun
c-tions \OT1/pcr/m/n/10.95 GeneralLowerBoundCoveringRadius
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[]\OT1/ptm/m/n/10.95 This com-mand can also be called us-ing the syn-tax \OT1/p
cr/m/n/10.95 LowerBoundCoveringRadiusSphereCovering(
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[]\OT1/ptm/m/n/10.95 This com-mand can also be called with \OT1/pcr/m/n/10.95 L
owerBoundCoveringRadiusEmbedded1( n, r
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[]\OT1/ptm/m/n/10.95 Sometimes \OT1/pcr/m/n/10.95 LowerBoundCoveringRadiusEmbed
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[]\OT1/ptm/m/n/10.95 This com-mand can also be called with \OT1/pcr/m/n/10.95 L
owerBoundCoveringRadiusEmbedded2( n, r
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[]\OT1/ptm/m/n/10.95 Sometimes \OT1/pcr/m/n/10.95 LowerBoundCoveringRadiusEmbed
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[]\OT1/ptm/m/n/10.95 If [] is a code-word, then \OT1/pcr/m/n/10.95 CodeDistance
Enumerator \OT1/ptm/m/n/10.95 re-turns the same poly-no-mial as
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[]\OT1/ptm/m/n/10.95 See also the \OT1/phv/m/n/10.95 GAP \OT1/ptm/m/n/10.95 fun
c-tion \OT1/pcr/m/n/10.95 RandomPrimitivePolynomial\OT1/ptm/m/n/10.95 , \OT1/pc
r/m/n/10.95 RandomPrimitivePolynomial
 []


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[136]
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[137]
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[138]
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[139]
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[140]
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! Missing $ inserted.
<inserted text> 
                $
l.7616 ... Guava. Same as \texttt{guava_version()}
                                                  . }
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Extra }, or forgotten $.
<recently read> \egroup 
                        
l.7616 ... Guava. Same as \texttt{guava_version()}
                                                  . }
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Extra }, or forgotten $.
l.7616 ...ava. Same as \texttt{guava_version()}. }
                                                  
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
l.7617 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.


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[141]
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[]\OT1/pcr/m/n/10.95 The function CoefficientToPolynomial returns the degree $\
OML/ptmcm/m/it/10.95 d \OMS/pzccm/m/n/10.95 ^^@ \OT1/ptmcm/m/n/10.95 1$ \OT1/pc
r/m/n/10.95 polynomial
 []


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\OML/ptmcm/m/it/10.95 c[] \OT1/ptmcm/m/n/10.95 + \OML/ptmcm/m/it/10.95 c[]x \OT
1/ptmcm/m/n/10.95 + \OML/ptmcm/m/it/10.95 ::: \OT1/ptmcm/m/n/10.95 + \OML/ptmcm
/m/it/10.95 c[]x[]$\OT1/pcr/m/n/10.95 , where [] is a list of elements of a fie
ld, $\OML/ptmcm/m/it/10.95 coeffs \OT1/ptmcm/m/n/10.95 =
 []


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[]\OT1/pcr/m/n/10.95 The function DegreesMonomialTerm returns the list of degre
es to which each
 []


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\OT1/pcr/m/n/10.95 variable in the multivariate polynomial ring [] occurs in th
e monomial [], where
 []

[142]
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[]\OT1/pcr/m/n/10.95 The function DivisorsMultivariatePolynomial returns the li
st of polynomial
 []


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\OT1/pcr/m/n/10.95 divisors of [] in the multivariate polynomial ring [] with c
oefficients in a
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\OT1/pcr/m/n/10.95 field. This program uses a simple but slow algorithm (see Jo
achim von zur
 []


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\OT1/pcr/m/n/10.95 Gathen, J[]urgen Gerhard, [[]][], exercise 16.10) which firs
t converts the
 []


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\OT1/pcr/m/n/10.95 multivariate polynomial [] to an associated univariate polyn
omial $\OML/ptmcm/m/it/10.95 f[]$\OT1/pcr/m/n/10.95 , then
 []


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\OT1/pcr/m/n/10.95 Factors $\OML/ptmcm/m/it/10.95 f[]$\OT1/pcr/m/n/10.95 , and 
finally converts these univariate factors back into the
 []


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\OT1/pcr/m/n/10.95 multivariate polynomial factors of []. Since Factors is non-
deterministic,
 []

(./guava.bbl (./guava.brf)
\tf@brf=\write8
\openout8 = `guava.brf'.

 [143]
! Missing { inserted.
<to be read again> 
                   $
l.13 
     
A left brace was mandatory here, so I've put one in.
You might want to delete and/or insert some corrections
so that I will find a matching right brace soon.
(If you're confused by all this, try typing `I}' now.)

! Missing } inserted.
<inserted text> 
                }
l.13 
     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

[144

]) (./guava.ind [145]
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[]\OT1/pcr/m/n/10.95 AClosestVectorComb..MatFFEVecFFECoords\OT1/ptm/m/n/10.95 ,

 []


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[]\OT1/pcr/m/n/10.95 AClosestVectorCombinationsMatFFEVecFFE\OT1/ptm/m/n/10.95 ,

 []


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[]\OT1/pcr/m/n/10.95 ActionMoebiusTransformationOnDivisorP1
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[]\OT1/pcr/m/n/10.95 ActionMoebiusTransformationOnFunction \OT1/ptm/m/n/10.95 ,

 []

[146

] [147]
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[]\OT1/pcr/m/n/10.95 IsActionMoebiusTransformationOnDivisorDefinedP1
 []


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[]\OT1/pcr/m/n/10.95 LowerBoundCoveringRadiusCountingExcess\OT1/ptm/m/n/10.95 ,

 []


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[]\OT1/pcr/m/n/10.95 LowerBoundCoveringRadiusSphereCovering\OT1/ptm/m/n/10.95 ,

 []


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[]\OT1/pcr/m/n/10.95 MatrixRepresentationOnRiemannRochSpaceP1
 []


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[]\OT1/pcr/m/n/10.95 MatrixTransformationOnMultivariatePolynomial
 []

[148] [149]
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[]\OT1/pcr/m/n/10.95 UpperBoundCoveringRadiusGriesmerLike\OT1/ptm/m/n/10.95 ,
 []

[150

]) (./guava.aux)

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