Work

Heights of error-correcting codes

Year: 2024

Type: article

Abstract: In this work, we investigate the evaluation of odd polynomials P defined on a finite field on the class of error-correcting codes C. We exploit the correspondence between codes and Tanner graphs. Thus, we formally define P(C), a polynomial code. Then the new notion of height of a code emerges, whose properties are studied. We extended the lower bound of Tanner on the minimum distance of a code to the case of a polynomial code, by using spectral graph theory. Computer algebra software enable us to give numerical results to illustrate the theory of polynomial codes for various classes of error-correcting codes.

Source: Gulf Journal of Mathematics

DOI: 10.56947/gjom.v18i2.2397

Authors: Saber Darmoun, Abdelmoumen Khalid, Ben-Azza Hussain

Institutions: Sidi Mohamed Ben Abdellah University, Université Moulay Ismail de Meknes

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4405172159

FWCI:

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