Work

Construction and Fast Decoding of Binary Linear Sum-Rank-Metric Codes

Year: 2025

Type: article

Abstract: Sum-rank-metric codes have wide applications in multishot network coding and distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp decoding algorithms have been proposed and studied. In this paper, we construct binary linear sum-rank-metric codes in F2×22⊕ F2×22⊕ . . . ⊕ F2×22from BCH, Goppa and additive quaternary codes. A reduction of decoding of binary sum-rank-metric codes to decoding of Hamming metric codes is given. Fast decoding algorithms of BCH-type and Goppa-type binary linear sum-rank-metric codes in F2×22⊕ F2×22⊕ . . . ⊕ F2×22with the block lengthl, which are better than these sum-rank BCH codes, are presented. These fast decoding algorithms for BCH-type and Goppa-type binary linear sum-rank-metric codes need at mostO(l2) operations in the field F4. Asymptotically good sequences of quadratic-time encodable and decodable binary linear sum-rank-metric codes with the matrix size 2×2 are constructed from Goppa codes.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2025.3619572

Authors: Hao Chen, Zhiqiang Cheng, Yanfeng Qi

Institutions: Jinan University, Jiangxi University of Finance and Economics, Hangzhou Dianzi University

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province

Awards: G6342790992, G6816960198