arXiv subjects

Qingfeng Xia

Publications and source records attributed to Qingfeng Xia.

3 recordsLinked to original sources

arXiv2026

Quasi-MSRD Codes and Their Properties

Sum-rank-metric codes have recently attracted considerable attention of many researchers, due to their applications in network coding, space-time codes and distributed storage. MSRD codes are those good codes attaining the Singleton bound in the sum-rank metric. However, MSRD codes do not exist for some dimensions. Motivated by this fact, we introduce the notion of quasi-MSRD (QMSRD) codes and provide some properties of them. What is more, we find that not every QMSRD code has a QMSRD dual code, so we give the definition of dually QMSRD codes, whose dual codes and themselves are both QMSRD. Finally, we characterize such codes, derive their support, rank-list and sum-rank distributions as well as compute their generalized sum-rank weights.

cs.IT↗

arXiv2025

Self-dual codes and LCD codes in sum-rank metric

Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based on the duality theory of sum-rank codes [Byrne, Gluesing-Luerssen, Ravagnani, IEEE TIT, 2021] and those related theory of rank-metric codes, it is significant to study self-dual codes and linear complementary dual (LCD) codes in sum-rank metric. In this paper, we introduce the notion of self-dual codes and LCD codes in sum-rank metric, and obtain two methods of constructing self-dual sum-rank codes and LCD sum-rank codes from Euclidean self-dual codes and Euclidean LCD codes. Some examples of cyclic self-dual sum-rank codes and cyclic LCD sum-rank codes with good parameters are provided. In addition, we prove that there exist asymptotically good self-dual sum-rank codes.

cs.IT↗

arXiv2023

Function-Correcting Codes for Symbol-Pair Read Channels

Function-correcting codes are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we extend function-correcting codes from binary symmetric channels to symbol-pair read channels. We introduce irregular-pair-distance codes and connect them with function-correcting symbol-pair codes. Using the connection, we derive general upper and lower bounds on the optimal redundancy of function-correcting symbol-pair codes. For ease of evaluation, we simplify these bounds and employ the simplified bounds to specific functions including pair-locally binary functions, pair weight functions and pair weight distribution functions.

cs.IT↗