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The weight distribution of indecomposable cyclic codes over 2-groups

1992
*
Journal of combinatorial theory. Series A
*

*weight*

*distribution*

*of*

*indecomposable*

*cyclic*

*codes*

*over*

*2*-

*groups*. ...

*indecomposable*

*cyclic*

*codes*

*over*

*2*-

*groups*. ... If a =

*2*" -1, then (Rad GF(

*2*") C2,,,)" is an m-fold even

*code*.

*2*. Otherwise let r be

*the*least index, 1 <r <m, so that a,=O. (a) Let CI,+~ = ... = a, = 0. ...

##
###
Page 2244 of Mathematical Reviews Vol. , Issue 87d
[page]

1987
*
Mathematical Reviews
*

*of*

*the*corresponding

*group*algebra

*of*

*the*finite

*cyclic*

*group*

*over*

*the*alphabet. ... ; Ward, Robert L. 87d:94043

*Weight*

*distributions*

*of*some irreducible

*cyclic*

*codes*. ...

##
###
Page 2924 of Mathematical Reviews Vol. , Issue 93e
[page]

1993
*
Mathematical Reviews
*

(D-BAYR)

*The**weight**distribution**of**indecomposable**cyclic**codes**over**2*-*groups*. ... From this characterization we obtain*the**weight**distribution**of*all*indecomposable*GF(*2*”)Czm-*codes*, and*the**weight**distribution**of**the*radical powers*of*GF(*2*”)G if G contains a normal*cyclic*Sylow*2*-subgroup ...##
###
Page 4873 of Mathematical Reviews Vol. 58, Issue 6
[page]

1979
*
Mathematical Reviews
*

Authors’ summary: “There are 26 distinct

*indecomposable*self- dual*codes**of*length 24*over*GF(*2*), including unique*codes**of*minimum*weights*8 and 6, whose*groups*are, respectively,*the*Mathieu*group*M, ... For each*code*we give*the*order*of*its*group*,*the*number*of*equivalent*codes*, and its*weight**distribution*.” 58 #33506 ...##
###
On ternary self-dual codes of length 24

1981
*
IEEE Transactions on Information Theory
*

A hstract-A partial classification is given

doi:10.1109/tit.1981.1056328
fatcat:6dsd7hecjnek7ew2iysdespxyy
*of**the*self-dual*codes**of*length 24*over*GF(3). ...*The*main results are as follows: there are exactly two*codes*with minimum Hamming distance d = 9; most*of**the**codes*have d = 6 and are*indecomposable*; one*code*with d = 6 has a trivial automorphism*group*... ACKNOWLEDGMENT*The*CAMAC computer system at*the*University*of*Illinois at Chicago Circle was used to find*the*automorphism*group*and other properties*of*these*codes*, and further processing*of**the**codes*...##
###
Page 3489 of Mathematical Reviews Vol. , Issue 93f
[page]

1993
*
Mathematical Reviews
*

Summary: “It is shown that linear

*cyclic*(q + 1, 3)-MDS*codes**over*GF(q) are unique but there exist $9(h) nonequivalent linear*cyclic*(q+ 1,4)-MDS*codes**over*GF(q) for gq =*2*", h > 3, where @ is*the*Euler ... Summary: “We characterize*the*automorphism*groups**of**the*Delsarte-Goethals*codes*DG(m,d) (m = 2t+*2*>6,2<d<t). ...##
###
Determining all indecomposable codes over some Hopf algebras

2011
*
Journal of Computational and Applied Mathematics
*

We determine all

doi:10.1016/j.cam.2010.07.014
fatcat:pboukr5cunamncconfpa6kwrei
*indecomposable**codes**over*a class*of*Hopf algebras named Taft Algebras. We calculate dual*codes*and tensor products*of*these*indecomposable**codes*and give applications*of*them. ... Second author was supported by a predoctoral fellowship*of**the*project Teoría de Anillos y Aplicaciones a la Geometría no Conmutativa (MTM2008-03339) from Ministerio de Ciencia e Innovación. ... As Berman in [3] observed,*cyclic**codes*and Reed-Muller*codes*can be seen as ideals in*the**group*ring KG (where K is a finite field and G is a finite*cyclic**group*). ...##
###
Page 5534 of Mathematical Reviews Vol. , Issue 94i
[page]

1994
*
Mathematical Reviews
*

*The*most familiar example is that

*of*a

*cyclic*

*code*C, with G

*cyclic*

*of*order n. ... For

*the*purposes

*of*this paper, a better example is furnished by

*the*binary Reed-Muller

*codes*

*of*length n =

*2*” with G an elementary abelian

*2*-

*group*

*of*order

*2*”. ...

##
###
Page 5761 of Mathematical Reviews Vol. , Issue 96i
[page]

1996
*
Mathematical Reviews
*

Our attention is focused mainly on

*indecomposable**cyclic**groups*(i.e.,*of*prime power order), since they are*the*elementary ‘building blocks’*of*any abelian*group*. ...*weight**of**the**code*. ...##
###
Page 4107 of Mathematical Reviews Vol. , Issue 92g
[page]

1992
*
Mathematical Reviews
*

*The*

*weight*

*distributions*are obtained by first considering

*the*dual

*codes*, which are related to a certain family

*of*elliptic curves

*over*

*the*finite field F,, and for which

*the*

*weights*are essentially

*the*... , Marcel (NL-LEID) Hecke operators and

*the*

*weight*

*distributions*

*of*certain

*codes*. ...

##
###
Self-dual codes over GF(4)

1978
*
Journal of combinatorial theory. Series A
*

This paper studies

doi:10.1016/0097-3165(78)90021-3
fatcat:vgoy2pbz7zd4djml2gediupdfu
*codes*V*over*GF(4) which have even*weights*and have*the*same*weight**distribution*as*the*dual*code*FL. Some*of**the*results are as follows. All such*codes*satisfy VL = 4. ...*The*number*of*such V's is determined, and those*of*length <14 are completely classified.*The**weight*enumerator*of*% is characterized and an upper bound obtained on*the*minimum distance. ... Sims for computing*the*orders*of*some permutation*groups*for us, and especially V. ...##
###
Self-dual codes overGF(3)andGF(4)of length not exceeding 16

1979
*
IEEE Transactions on Information Theory
*

Abstmct-All self-dual

doi:10.1109/tit.1979.1056047
fatcat:cfcdd6mmz5c2zdpzziqhq3jj7e
*codes**over*GF (3) and GF(4)*of*length 16 are found.*The*sehlual*codes**of*shorter length are described in a concise and systematic nut&ion. ... A number*of*new te&niques ("promotion" and "demotion," 'hggiq" and "subtraction") sre given for constm%ng*codes*. ... ACKNOWLEDGMENT*The*CAMAC system at*the*University*of*Illinois at Chicago Circle Computer Center was used to compute various properties*of*these*codes*and*groups*. J. H. ...##
###
On the classification and enumeration of self-dual codes

1975
*
Journal of combinatorial theory. Series A
*

For each

doi:10.1016/0097-3165(75)90042-4
fatcat:pmntwe3hsrgrbgo63xbkvkbuci
*code*we give*the*order*of*its*group*,*the*number*of**codes*equivalent to it, and its*weight**distribution*. There is a unique [24, 12, 61 selfdual*code*. ... Several theorems on*the*enumeration*of*self-dual*codes*are used, including formulas for*the*number*of*such*codes*with minimum distance > 4, and for*the*sum*of**the**weight*enumerators*of*all such*codes**of*... Conway for telling us about his enumeration*of**the*self-dual*codes**of*length 24 with*weights*divisible by 4. In*the*course*of*this work we have used*the*...##
###
Page 6763 of Mathematical Reviews Vol. , Issue 88m
[page]

1988
*
Mathematical Reviews
*

Each

*code*is described by a generator matrix; its Hamming*weight**distribution*and*the*order*of*its ... Let a, denote*the*number*of*cosets*of**the*(*2*”,m-+ 1) Reed- Muller*code*with minimum*weight*n. ...##
###
Directed graph representation of half-rate additive codes over GF(4)

2010
*
Designs, Codes and Cryptography
*

Graph representation reduces

doi:10.1007/s10623-010-9469-6
fatcat:ncgvof3mvvfonca6zygeqwkuqm
*the*complexity*of**code*classification, and enables us to classify additive (n,*2*^n)*codes**over*GF(4)*of*length up to 7. ... We show that (n,*2*^n) additive*codes**over*GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive*codes**over*GF(4), which correspond to undirected graphs. ... Acknowledgement*The*authors would like to thank Jürgen Bierbrauer for helpful comments. This research was supported by*the*Research Council*of*Norway. ...
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