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

2002
*
IEEE Transactions on Information Theory
*

Using a particular construction

doi:10.1109/tit.2002.1013146
fatcat:iew3vhmygfg2volkqlaamcloa4
*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. ...##
###
Quantum codes from cyclic codes over GF(4^m)
[article]

2000
*
arXiv
*
pre-print

We also provide examples

arXiv:quant-ph/0008129v1
fatcat:4unxtcjttzb67ojixte3tge544
*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. ...##
###
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]

2015
*
arXiv
*
pre-print

We investigate

arXiv:1504.07831v1
fatcat:33fvcqim7bag5ilhxymhurwtwu
*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. ...##
###
Quasi-Cyclic Complementary Dual Code
[article]

2015
*
arXiv
*
pre-print

Hermitian LCD

arXiv:1506.01971v1
fatcat:5ywoz2w6tffrfnxlmx3dimed6m
*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. ...##
###
The Complexity Limits of Graphical Models for Linear Codes

2007
*
2007 IEEE Information Theory Workshop
*

Since

doi:10.1109/itw.2007.4313064
fatcat:znh4zgn3r5cx7ez7yvilnvylvm
*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. ...##
###
Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$

2015
*
Journal of Algebra Combinatorics Discrete Structures and Applications
*

We investigate

doi:10.13069/jacodesmath.90080
fatcat:dmcljs5iuneiphes24ieymyvfy
*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. ...##
###
Self-orthogonality of q-ary Images of q^m-ary Codes and Quantum Code Construction
[article]

2007
*
arXiv
*
pre-print

In this work, a generalized version

arXiv:cs/0606106v3
fatcat:tsyllhxrrvdkvfhfrdowbtfgjq
*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*. ...##
###
A class of constacyclic codes over Fp+vFp and its Gray image

2011
*
Discrete Mathematics
*

We introduce a Gray map from F p + vF p to F 2 p and study (1 − 2v)-constacyclic

doi:10.1016/j.disc.2011.08.015
fatcat:jpxq5hkeifevdobkodftnfhztm
*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. ...##
###
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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