Weighted Hamming Metric Structures

02/04/2018
by   Bora Moon, et al.
0

A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the extended binary Hamming code to be perfect codes in the weighted Hamming metric. And, we also give some structures of a 2-perfect code and how to construct a 2-perfect code in some weighted Hamming metric.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/11/2021

On q-ary shortened-1-perfect-like codes

We study codes with parameters of q-ary shortened Hamming codes, i.e., (...
research
12/03/2020

On extended 1-perfect bitrades

We prove the equivalence of several definitions of extended 1-perfect bi...
research
10/15/2017

Stable Matchings in Metric Spaces: Modeling Real-World Preferences using Proximity

Suppose each of n men and n women is located at a point in a metric spac...
research
03/08/2021

Geometrical Representation for Number-theoretic Transforms

This short note introduces a geometric representation for binary (or ter...
research
01/10/2019

Graph embeddings into Hamming spaces

Graph embeddings deal with injective maps from a given simple, undirecte...
research
01/06/2022

A simple coding-decoding algorithm for the Hamming code

In this work, we present a new simple way to encode/decode messages tran...
research
08/21/2023

Smoothing of binary codes, uniform distributions, and applications

The action of a noise operator on a code transforms it into a distributi...

Please sign up or login with your details

Forgot password? Click here to reset