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The q-ary image of some q/sup m/-ary cyclic codes: permutation group and soft-decision decoding

J. Lacan, E. Delpeyroux
2002 IEEE Transactions on Information Theory  
Using a particular construction of generator matrices of the -ary image of -ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups.  ...  Index Terms-Permutation groups, -ary image of -ary cyclic codes, soft-decision decoding.  ...  Lin for the preprint of their paper [16]. The authors also wish to thank R. Koetter for his helpful comments on the drafting of this correspondence.  ... 
doi:10.1109/tit.2002.1013146 fatcat:iew3vhmygfg2volkqlaamcloa4

Quantum codes from cyclic codes over GF(4^m) [article]

Andrew Thangaraj, Steven McLaughlin
2000 arXiv   pre-print
We also provide examples of these codes some of which meet the known bounds for quantum codes.  ...  We provide a construction for quantum codes (hermitian-self-orthogonal codes over GF(4)) starting from cyclic codes over GF(4^m).  ...  Acknowledgement The authors wish to thank Dr. Eric M. Rains, AT&T Research, for his help with interpretations in [1] and the two reviewers for providing helpful comments.  ... 
arXiv:quant-ph/0008129v1 fatcat:4unxtcjttzb67ojixte3tge544

Page 3759 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
The underlying codes are cyclic codes.” 2002e:94128 94B15 11T71 Mouaha, Christophe; Schiffels, Gerhard (D-BLFM; Bielefeld) All q’"-ary cyclic codes with cyclic g-ary image are known.  ...  This paper complements these earlier papers, gives a full answer to the characterization problem, and shows that there are no more g”-ary cyclic codes with cyclic q-ary image than those given by Séguin  ... 

Page 3223 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
In this paper the author considers (mn,mk) cyclic codes over GF(q) which are q-ary images of (n,k) cyclic codes over GF(q™).  ...  Among the many consequences deduced from this theorem, the author obtains a complete characterization of cyclic codes over GF(q) which are q-ary images of cyclic codes over GF(g’): the generator poly-  ... 

Page 5762 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
If V is a q”-ary [n, k] cyclic code, its q- ary image with respect to the basis a is d,(V), where d,(V) = {d,(a(z)): a(z) € V}.  ...  a q”’-ary cyclic code.  ... 

Page 2050 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
Summary: “For (n,q) = p’, where p=ch(F,), s >1, and V is a q”-ary repeated-root cyclic code of length n with generator polynomial g(x), we give a partial answer about whether the g- ary image of V is cyclic  ...  Petersburg) 98c:94029 94B15 Tang, Li-zhong [Tang, Li Zhong” (SGP-NANT-EE; Singapore) ; Soh, Cheong Boon (SGP-NANT-EE; Singapore); Gunawan, Erry (SGP-NANT-EE; Singapore) A note on the q-ary image of a g  ... 

Page 973 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Stepanov (TR-BILKS; Ankara) 2000b:11137 11T71 94B15 Lacan, Jéréme (F-TOUL3-AA; Toulouse); Delpeyroux, Emmanuelle (F-TOUL3-AA; Toulouse) Permutation group of the g-ary image of some q”’-ary cyclic codes  ...  Moreover, under the above assumption, when (N,m) = 1 the g-ary image of C is equivalent to a cyclic code. {For the entire collection see MR 99f:11002.}  ... 

Page 5700 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews  
Summary: “Using a particular construction of generator matri- ces of the g-ary image of g’’-ary cyclic codes, it is proved that some of these codes are invariant under the action of particu- lar permutation  ...  Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials.” 2003¢:94056 94B15 94B35 Lacan, Jéréime; Delpeyroux, Emmanuelle The qg-ary image of some g’  ... 

Skew Cyclic codes over _q+u_q+v_q+uv_q [article]

Ting Yao, Minjia Shi, Patrick Solé
2015 arXiv   pre-print
We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.  ...  In this paper, we study skew cyclic codes over the ring R=_q+u_q+v_q+uv_q, where u^2=u,v^2=v,uv=vu, q=p^m and p is an odd prime.  ...  First, we introduce the structure of linear codes over R and show the structural properties of skew cyclic codes over R.  ... 
arXiv:1504.07831v1 fatcat:33fvcqim7bag5ilhxymhurwtwu

Quasi-Cyclic Complementary Dual Code [article]

Cem Güneri̇, Buket Özkaya, Patrick Solé
2015 arXiv   pre-print
Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized. Constructions of QCCD codes from codes over larger alphabets are given.  ...  LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure.  ...  Background on Quasi-Cyclic Codes In the whole paper q denotes a prime power and F q the finite field of that order.  ... 
arXiv:1506.01971v1 fatcat:5ywoz2w6tffrfnxlmx3dimed6m

The Complexity Limits of Graphical Models for Linear Codes

Thomas R. Halford, Keith M. Chugg
2007 2007 IEEE Information Theory Workshop  
Since the discovery of turbo codes in the 1990s, much of the work concerning graphical models for codes has focused on constructing models in order to define a new code.  ...  This work focuses on the theoretical foundations of the inverse problem to code construction -extracting a graphical model for a given (fixed) code.  ...  Specifically, let G C be a q m -ary graphical model for the linear code C over F q defined on an index set I.  ... 
doi:10.1109/itw.2007.4313064 fatcat:znh4zgn3r5cx7ez7yvilnvylvm

Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$

Ting Yao, Minjia Shi, Patrick Solé
2015 Journal of Algebra Combinatorics Discrete Structures and Applications  
We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.  ...  In this paper, we study skew cyclic codes over the ring R = Fq + uFq + vFq + uvFq, where u 2 = u, v 2 = v, uv = vu, q = p m and p is an odd prime.  ...  Later, in [4] , some important results on the duals of the skew cyclic codes over F q [x; θ] are given. In [12] , I. Siap et al. presented the structure of skew cyclic codes of arbitrary length.  ... 
doi:10.13069/jacodesmath.90080 fatcat:dmcljs5iuneiphes24ieymyvfy

Self-orthogonality of q-ary Images of q^m-ary Codes and Quantum Code Construction [article]

Sundeep B, Andrew Thangaraj
2007 arXiv   pre-print
In this work, a generalized version of the problem of self-orthogonality of the q-ary image of a q^m-ary code has been considered.  ...  The properties of such an image depend on the original code and the basis chosen for imaging.  ...  QUANTUM CODE CONSTRUCTION In this section, we specialize our results to cyclic codes and construct new quantum BCH codes from 4-ary images of 4 m -ary codes.  ... 
arXiv:cs/0606106v3 fatcat:tsyllhxrrvdkvfhfrdowbtfgjq

A class of constacyclic codes over Fp+vFp and its Gray image

Shixin Zhu, Liqi Wang
2011 Discrete Mathematics  
We introduce a Gray map from F p + vF p to F 2 p and study (1 − 2v)-constacyclic codes over It is proved that the image of a (1−2v)-constacyclic code of length n over F p + vF p under the Gray map is a  ...  distance-invariant linear cyclic code of length 2n over F p .  ...  Acknowledgments The authors would like to thank the referees for their helpful comments and a very meticulous reading of this manuscript.  ... 
doi:10.1016/j.disc.2011.08.015 fatcat:jpxq5hkeifevdobkodftnfhztm

Page 2947 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
Next we find all constacyclic codes whose q-ary images are by a Tschirnhaus transformation isomorphic to shortened cyclic codes.  ...  We find sufficient conditions under which the minimal distance of such a code is equal to three.” 99d:94038 94B15 Jensen, Jorn M. (DK-TUD; Lyngby) On the g-ary image of cyclic codes.  ... 
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