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The weight distribution of indecomposable cyclic codes over 2-groups

Karl-Heinz Zimmermann
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.  ... 
doi:10.1016/0097-3165(92)90039-w fatcat:2za7rs7dqzanfjbf6vyucl4wpq

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

J. Leon, V. Pless, N. Sloane
1981 IEEE Transactions on Information Theory  
A hstract-A partial classification is given 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  ... 
doi:10.1109/tit.1981.1056328 fatcat:6dsd7hecjnek7ew2iysdespxyy

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

J. Cuadra, J.M. García-Rubira, J.A. López-Ramos
2011 Journal of Computational and Applied Mathematics  
We determine all 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).  ... 
doi:10.1016/ fatcat:pboukr5cunamncconfpa6kwrei

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)

F.J MacWilliams, A.M Odlyzko, N.J.A Sloane, H.N Ward
1978 Journal of combinatorial theory. Series A  
This paper studies 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.  ... 
doi:10.1016/0097-3165(78)90021-3 fatcat:vgoy2pbz7zd4djml2gediupdfu

Self-dual codes overGF(3)andGF(4)of length not exceeding 16

J. Conway, V. Pless, N. Sloane
1979 IEEE Transactions on Information Theory  
Abstmct-All self-dual 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.  ... 
doi:10.1109/tit.1979.1056047 fatcat:cfcdd6mmz5c2zdpzziqhq3jj7e

On the classification and enumeration of self-dual codes

Vera Pless, N.J.A Sloane
1975 Journal of combinatorial theory. Series A  
For each 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  ... 
doi:10.1016/0097-3165(75)90042-4 fatcat:pmntwe3hsrgrbgo63xbkvkbuci

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)

Lars Eirik Danielsen, Matthew G. Parker
2010 Designs, Codes and Cryptography  
Graph representation reduces 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.  ... 
doi:10.1007/s10623-010-9469-6 fatcat:ncgvof3mvvfonca6zygeqwkuqm
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