On Rank and MDR Cyclic Codes of Length Over
A Garg, S Dutt - Conference on Algorithms and Discrete Applied …, 2017 - Springer
A Garg, S Dutt
Conference on Algorithms and Discrete Applied Mathematics, 2017•SpringerIn this paper, a set of generators (in a unique from) called the distinguished set of
generators, of a cyclic code C of length n= 2^ kn= 2 k (where k is a natural number) over Z_8
Z 8 is obtained. This set of generators is used to find the rank of the cyclic code C. It is
proved that the rank of a cyclic code C of length n= 2^ kn= 2 k over Z_8 Z 8 is equal to nv nv,
where v is the degree of a minimal degree polynomial in C. Then a description of all MHDR
(maximum hamming distance with respect to rank) cyclic codes of length n= 2^ kn= 2 k over …
generators, of a cyclic code C of length n= 2^ kn= 2 k (where k is a natural number) over Z_8
Z 8 is obtained. This set of generators is used to find the rank of the cyclic code C. It is
proved that the rank of a cyclic code C of length n= 2^ kn= 2 k over Z_8 Z 8 is equal to nv nv,
where v is the degree of a minimal degree polynomial in C. Then a description of all MHDR
(maximum hamming distance with respect to rank) cyclic codes of length n= 2^ kn= 2 k over …
Abstract
In this paper, a set of generators (in a unique from) called the distinguished set of generators, of a cyclic code C of length (where k is a natural number) over is obtained. This set of generators is used to find the rank of the cyclic code C. It is proved that the rank of a cyclic code C of length over is equal to , where v is the degree of a minimal degree polynomial in C. Then a description of all MHDR (maximum hamming distance with respect to rank) cyclic codes of length over is given. An example of the best codes over of length 4 having largest minimum Hamming, Lee and Euclidean distances among all codes of the same rank is also given.
Springer
以上显示的是最相近的搜索结果。 查看全部搜索结果