The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Peta Kelabu umum untuk kod di atas gelanggang Fq[u]/ut+1> diperkenalkan, di mana q=pm adalah kuasa utama. Ia ditunjukkan bahawa imej kelabu umum bagi panjang linear-N (1-ut)-kod kitaran tamat Fq[u]/ut+1> ialah panjang linear invarian jarak-qtN kod indeks kuasi kitaran qt/p lebih Fq. Ternyata jika (N,p)=1 maka setiap kod linear berakhir Fq itu ialah imej Kelabu umum bagi panjang-N kod kitaran tamat Fq[u]/ut+1>, juga bersamaan kepada panjang linear-qtN kod indeks kuasi kitaran qt/p lebih Fq. Hubungan antara panjang linear-pN kod kitaran dengan (N,p)=1 lebih Fp dan kod kitaran panjang linear-N di atas Fp+uFp ditentukan secara jelas.
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Salinan
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
Salinan
@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},}
Salinan
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 -