Work

Linear Complementary Dual Codes and Linear Complementary Pairs of AG Codes in Function Fields

Year: 2024

Type: article

Abstract: In recent years, linear complementary pairs (LCPs) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory and cryptography. In this work, we construct explicit LCPs of codes and LCD codes from function fields of genus$g \geq 1$. To accomplish this, we present pairs of suitable divisors that give rise to non-special divisors of degree$g-1$in the function field. The results are applied in constructing LCPs of algebraic geometry codes and LCD algebraic geometry (AG) codes in Kummer extensions, hyperelliptic function fields, and elliptic curves.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2024.3521094

Authors: Alonso S. Castellanos, Adler V. Marques, Luciane Quoos

Institutions: Universidade Federal de Uberlândia, Universidade Federal do Rio de Janeiro

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do Estado de Minas Gerais

Awards: G1846376527, SEMIGRUPO DE WEIERSTRASS EM M PONTOS E PESOS GENERALIZADOS DE HAMMING SOBRE CURVAS DO TIPO KUMMER, G7897147747