On the construction of some optimal polynomial codes

Authors:
Yajing Li;Weihong Chen
Affiliations:
Department of Applied Mathematics, Information Engineering University, Zhengzhou, China;Department of Applied Mathematics, Information Engineering University, Zhengzhou, China
Venue:
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part II
Year:
2005

Citing 3
Cited 0

Introduction to Coding Theory

Introduction to Coding Theory
A class of linear codes with good parameters

IEEE Transactions on Information Theory
Symmetric Polynomials and Some Good Codes

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We generalize the idea of constructing codes over a finite field Fqby evaluating a certain collection of polynomials at elements of an extension field of Fq. Our approach for extensions of arbitrary degrees is different from the method in [3]. We make use of a normal element and circular permutations to construct polynomials over the intermediate extension field between Fqand F$_{q^{t}}$denoted by F$_{q^{s}}$where s divides t. It turns out that many codes with the best parameters can be obtained by our construction and improve the parameters of Brouwer’s table [1]. Some codes we get are optimal by the Griesmer bound.