Linear Complementary dual codes and Linear Complementary pairs of AG codes in function fields
<|reference_start|>Linear Complementary dual codes and Linear Complementary pairs of AG codes in function fields: In recent years, linear complementary pairs (LCP) 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 giving 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.<|reference_end|>
@article{castellanos2024linear,
    title={Linear Complementary dual codes and Linear Complementary pairs of AG
  codes in function fields},
    author={Alonso S. Castellanos, Adler V. Marques, and Luciane Quoos},
    journal={arXiv preprint arXiv:2407.05845},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.05845},
    primaryClass={math.AG cs.IT math.IT}
}