Euclidean and Hermitian Self-orthogonal Algebraic Geometry Codes and Their Application to Quantum Codes

2013/08/16 by Lingfei Jin, Chaoping Xing, Jin, Lingfei +1 · 4 citations
Computer Science · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.1308.3575

openalex publication_date 2013/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we show that if the dimension of an arbitrary algebraic geometry code over a finite field of even characters is slightly less than half of its length, then it is equivalent to an Euclidean self-orthogonal code. However, in the literatures, a strong contrition about existence of certain differential is required to obtain such a result. We also show a similar result on Hermitian self-orthogonal algebraic geometry codes. As a consequence, we can apply our result to quantum codes and obtain quantum codes with good asymptotic bounds.

Cited by

• Shortest self-orthogonal embeddings of binary linear codes
• The (+)-(L, P)-TGRS code
• A recursive approach to the construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic
• Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic

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