Constructions of MDS symbol-pair codes with minimum distance seven or eight

• Published in: Designs, codes, and cryptography Vol. 90; no. 10; pp. 2337 - 2359
• Main Authors: Ma, Junru, Luo, Jinquan
• Format: Journal Article
• Language: English
• Published: New York Springer US 2022; Springer Nature B.V
• Subjects: Coding and Information Theory; Computer Science; Cryptology; Discrete Mathematics in Computer Science; Error correction; 94B15; Constacyclic codes; Repeated-root cyclic codes; MDS symbol-pair codes; Minimum symbol-pair distance; 94B05
• ISSN: 0925-1022; 1573-7586
• DOI: 10.1007/s10623-022-01081-9

Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance plays a vital role in determining the error-correcting capability and the constructions of symbol-pair codes with largest possible minimum symbol-pair distance is of great importance. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that such codes can acheive the Singleton bound. In this paper, for length 5 p , two new classes of MDS symbol-pair codes with minimum symbol-pair distance seven or eight are constructed by utilizing repeated-root cyclic codes over F p , where p is a prime. In addition, we derive a class of MDS symbol-pair codes with minimum symbol-pair distance seven and length 4 p .