Paper Info
Title
On explicit minimum weight bases for extended cyclic codes related to Gold functions.
Abstract
Minimum weight bases of some extended cyclic codes can be chosen from the affine orbits of certain explicitly represented minimum weight codewords. We find such bases for the following three classes of codes: the extended primitive 2-error correcting BCH code of length \(n=2^m,\) where \(m\ge 4\) (for \(m\ge 20\) the result was proven in Grigorescu and Kaufman IEEE Trans Inf Theory 58(I. 2):78–81, 2011), the extended cyclic code \(\bar{C}_{1,5}\) of length \(n=2^m,\) odd m,  \(m\ge 5,\) and the extended cyclic codes \(\bar{C}_{1,2^i+1}\) of lengths \(n=2^m,\) \((i,\,m)=1\) and \(3\le i\le \frac{m-5}{4}-o(m).\)
Year
DOI
Venue
2018
10.1007/s10623-018-0464-7
Des. Codes Cryptography
Keywords
Field
DocType
Cyclic codes, Gold function, Minimal weight basis, Explicit basis, 94B15, 94A60
Discrete mathematics,Combinatorics,Cyclic code,BCH code,Minimum weight,Mathematics
Journal
Volume
Issue
ISSN
86
11
0925-1022
Citations 
PageRank 
References 
0
0.34
5
Authors
2
Name
Order
Citations
PageRank
Ivan Yu. Mogilnykh1368.74
Faina I. Solov'eva25914.78