Some Constacyclic and Cyclic Codes Over Fq[u]/<ut+1>
Summary :
A generalized Gray map for codes over the ring Fq[u]/<ut+1> is introduced, where q=pm is a prime power. It is shown that the generalized Gray image of a linear length-N (1-ut)-cyclic code over Fq[u]/<ut+1> is a distance-invariant linear length-qtN quasi-cyclic code of index qt/p over Fq. It turns out that if (N,p)=1 then every linear code over Fq that is the generalized Gray image of a length-N cyclic code over Fq[u]/<ut+1>, is also equivalent to a linear length-qtN quasi-cyclic code of index qt/p over Fq. The relationship between linear length-pN cyclic codes with (N,p)=1 over Fp and linear length-N cyclic codes over Fp+uFp is explicitly determined.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.4 pp.808-813
- Publication Date
- 2010/04/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E93.A.808
- Type of Manuscript
- PAPER
- Category
- Coding Theory
Authors
Keyword
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Reza SOBHANI, Morteza ESMAEILI, "Some Constacyclic and Cyclic Codes Over Fq[u]/
Abstract: A generalized Gray map for codes over the ring Fq[u]/<ut+1> is introduced, where q=pm is a prime power. It is shown that the generalized Gray image of a linear length-N (1-ut)-cyclic code over Fq[u]/<ut+1> is a distance-invariant linear length-qtN quasi-cyclic code of index qt/p over Fq. It turns out that if (N,p)=1 then every linear code over Fq that is the generalized Gray image of a length-N cyclic code over Fq[u]/<ut+1>, is also equivalent to a linear length-qtN quasi-cyclic code of index qt/p over Fq. The relationship between linear length-pN cyclic codes with (N,p)=1 over Fp and linear length-N cyclic codes over Fp+uFp is explicitly determined.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.808/_p
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@ARTICLE{e93-a_4_808,
author={Reza SOBHANI, Morteza ESMAEILI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Some Constacyclic and Cyclic Codes Over Fq[u]/
year={2010},
volume={E93-A},
number={4},
pages={808-813},
abstract={A generalized Gray map for codes over the ring Fq[u]/<ut+1> is introduced, where q=pm is a prime power. It is shown that the generalized Gray image of a linear length-N (1-ut)-cyclic code over Fq[u]/<ut+1> is a distance-invariant linear length-qtN quasi-cyclic code of index qt/p over Fq. It turns out that if (N,p)=1 then every linear code over Fq that is the generalized Gray image of a length-N cyclic code over Fq[u]/<ut+1>, is also equivalent to a linear length-qtN quasi-cyclic code of index qt/p over Fq. The relationship between linear length-pN cyclic codes with (N,p)=1 over Fp and linear length-N cyclic codes over Fp+uFp is explicitly determined.},
keywords={},
doi={10.1587/transfun.E93.A.808},
ISSN={1745-1337},
month={April},}
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TY - JOUR
TI - Some Constacyclic and Cyclic Codes Over Fq[u]/
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 808
EP - 813
AU - Reza SOBHANI
AU - Morteza ESMAEILI
PY - 2010
DO - 10.1587/transfun.E93.A.808
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2010
AB - A generalized Gray map for codes over the ring Fq[u]/<ut+1> is introduced, where q=pm is a prime power. It is shown that the generalized Gray image of a linear length-N (1-ut)-cyclic code over Fq[u]/<ut+1> is a distance-invariant linear length-qtN quasi-cyclic code of index qt/p over Fq. It turns out that if (N,p)=1 then every linear code over Fq that is the generalized Gray image of a length-N cyclic code over Fq[u]/<ut+1>, is also equivalent to a linear length-qtN quasi-cyclic code of index qt/p over Fq. The relationship between linear length-pN cyclic codes with (N,p)=1 over Fp and linear length-N cyclic codes over Fp+uFp is explicitly determined.
ER -
English
