AI Chat AI Image Generator AI Video Text to Speech

The weight distribution of codes over finite chain rings

10/27/2022

∙

by Giulia Cavicchioni, et al.

∙

∙

In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code. Thanks to these relations we are able to compute the full weight distribution of codes with small Singleton defects, such as MDS, MDR and AMDR codes.

Giulia Cavicchioni
1 publication
Alessio Meneghetti
16 publications

page 1

page 2

page 3

page 4

research

∙ 03/31/2020

A formula on the weight distribution of linear codes with applications to AMDS codes

The determination of the weight distribution of linear codes has been a ...

0 Alessio Meneghetti, et al. ∙

research

∙ 04/17/2018

The Subfield Codes of Hyperoval and Conic codes

Hyperovals in (2,(q)) with even q are maximal arcs and an interesting re...

0 Ziling Heng, et al. ∙

research

∙ 11/29/2017

F_q[G]-modules and G-invariant codes

If F_q is a finite field and G is a subgroup of the linear automorphisms...

0 Elias Javier Garcia Claro, et al. ∙

research

∙ 11/08/2022

The (+)-extended twisted generalized Reed-Solomon code

In this paper, we give a parity check matrix for the (+)-extended twiste...

0 Canze Zhu, et al. ∙

research

∙ 03/30/2021

Generalized b-weights and b-MDS Codes

In this paper, we first introduce the notion of generalized b-weights of...

0 Xu Pan, et al. ∙

research

∙ 03/23/2019

On the Maximum Number of Codewords of X-Codes of Constant Weight Three

X-codes form a special class of linear maps which were originally introd...

0 Yu Tsunoda, et al. ∙

research

∙ 06/17/2021

Density of Free Modules over Finite Chain Rings

In this paper we focus on modules over a finite chain ring ℛ of size q^s...

0 Eimear Byrne, et al. ∙