Self-orthogonal and self-dual codes from maximal curves

2025/01/14 by Wang, Puyin, Luo, Jinquan · 1 citation
#94B27 #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2501.16343

Abstract

In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing algebraic structure of finite fields and geometric properties of algebraic curves. Moreover, we construct self-orthogonal and self-dual codes with parameters [n, k, d]_q² satisfying k + d is close to n. Additionally, quantum codes with large minimum distance are also constructed.

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