由NMDS码构造的具有大最小距离的Plotkin最优纯量子LRC
Plotkin-optimal pure quantum LRCs with large minimum distances from NMDS codes
Yang Li, Shitao Li, Gaojun Luo, San Ling
AI 速览：该文提出从Hermitian对偶包含的NMDS码构造达到Plotkin类界的纯量子局部可恢复码（qLRC）的一般框架，并基于ESGRS码给出四族构造。
Quantum locally recoverable codes (qLRCs) are a class of quantum error-correcting codes that can recover an erased qudit by accessing only a few other qudits. This paper develops a general framework for constructing optimal pure qLRCs that attain the Plotkin-like bound, referred to as Plotkin-optimal pure qLRCs, from Hermitian dual-containing near maximum-distance separable (NMDS) codes. Focusing on a special class of NMDS codes called extended subcodes of generalized Reed-Solomon (ESGRS) codes, we determine their localities by analyzing certain subset sum problems over finite fields. By further exploiting the algebraic structures of ESGRS codes and related codes, we construct four families of Plotkin-optimal pure qLRCs with large lengths and more flexible minimum distances than existing constructions. These constructions provide strong global error-correction capability while retaining local recovery. To the best of our knowledge, they give the first families of qLRCs attaining the pure Plotkin-like bound. In addition, by using the resulting locality property, we resolve in the negative a related problem on ESGRS codes supporting combinatorial designs.