arXiv subjects

Zhao Chang-An

Publications and source records attributed to Zhao Chang-An.

2 recordsLinked to original sources

arXiv2025

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions

This paper introduces new constructions of sum-rank metric codes derived from algebraic function fields, as existing results on such codes remain limited. A major challenge lies in the determination of their parameters. We address this issue by employing quadratic Galois extensions, proposing two general constructions of $2\times2$ sum-rank codes. Analogous to algebraic geometry codes in the Hamming metric, our codes achieve a larger block length compared to existing constructions. We determine explicit parameters including dimensions and minimum distances of our codes, and we present an illustrative example using elliptic function fields. Finally, we discuss the asymptotic behavior of our codes and compare them with the Gilbert-Varshamov-like bound for sum-rank metric codes.

cs.IT↗

arXiv2025

Linear Complementary Pairs of Algebraic Geometry Codes via Kummer Extensions

Due to their widespread applications, linear complementary pairs (LCPs) have attracted much attention in recent years. In this paper, we determine explicit construction of non-special divisors of degree $g$ and $g-1$ on Kummer extensions with specific properties. In addition, we present several methods for constructing LCPs of algebraic geometry codes (AG Codes) via Kummer extensions. These results are applied in constructing explicit LCPs of AG Codes from subcovers of the BM curve, elliptic function fields, hyperelliptic function fields and other function fields. It is important to mention that we construct several families LCPs of MDS AG Codes from elliptic function fields and we obtain some linear complementary dual (LCD) codes from certain maximal elliptic function fields and hyperelliptic function fields.

cs.IT↗