Weight distribution of a class of cyclic codes of length $2^n$

Year 2019, Volume: 6 Issue: 1, 1 - 11, 19.01.2019

Manjit Singh , Sudhir Batra

https://doi.org/10.13069/jacodesmath.505364

Cited By: 1

Abstract

Let $\mathbb{F}_q$ be a finite field with $q$ elements and $n$ be a positive integer. In this paper, we determine the weight distribution of a class cyclic codes of length $2^n$ over $\mathbb{F}_q$ whose parity check polynomials are either binomials or trinomials with $2^l$ zeros over $\mathbb{F}_q$, where integer $l\ge 1$. In addition, constant weight and two-weight linear codes are constructed when $q\equiv3\pmod 4$.

Keywords

Linear codes, Reversible codes, Weight distributions, Constant weight codes

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