PMDS Array Codes Based on Punctured λ-twisted Circulant Matrices with Lower Complexity
Year: 2026
Type: conference-paper
Abstract: Partial maximum distance separable (PMDS) codes have attracted significant attention due to their ability to balance local recoverability and overall erasure protection. A (μ, n, r, s)-PMDS code consists of μn nodes divided into μ local groups of size n, where each group contains r local parities, while s additional global parities are introduced to strengthen the erasure-correction capability of the overall code. Constructing PMDS codes over small finite fields is highly desirable, as the field size directly affects the computational complexity of practical encoding and decoding. In this paper, motivated by the fact that punctured λ-twisted circulant matrices can effectively reduce computational complexity, we construct PMDS codes based on this structure. We generalize two existing PMDS array constructions. The first construction is implemented over ${{\mathbb{F}}_2}$ and requires only XOR operations and cyclic shifts. The second construction can reduce the computational complexity.
Institutions: Tsinghua University, Dongguan University of Technology
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204191000