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Two-Weight and a Few Weights Trace Codes over \mathbbFq+u\mathbbFq

2017/03/15 by Hongwei Liu, Liu, Hongwei, Youcef Maouche +1
Computer Science · Engineering · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1703.04968

openalex publication_date 2017/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number, q=ps for a positive integer s. For any positive divisor e of q-1, we construct an infinite family codes of size q2m with few Lee-weight. These codes are defined as trace codes over the ring R=\mathbbFq + u\mathbbFq, u2 = 0. Using Gauss sums, their Lee weight distributions are provided. When gcd(e,m)=1, we obtain an infinite family of two-weight codes over the finite field \mathbbFq which meet the Griesmer bound. Moreover, when gcd(e,m)=2, 3 or 4 we construct new infinite family codes with at most five-weight.

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