MDS, Near-MDS or 2-MDS Self-Dual Codes via Twisted Generalized Reed-Solomon Codes
Junzhen Sui, Qin Yue, Xia Li, Daitao Huang
Abstract
Twisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are non-equivalent to generalized Reed-Solomon (GRS) codes. In this paper, we characterize a sufficient and necessary condition that a twisted Reed-Solomon (TRS) code with two twists is MDS; give a sufficient and necessary condition that a TGRS code with two twists is self-dual, and present some constructions of self-dual TGRS codes. These self-dual codes are MDS, NMDS or 2-MDS. Furthermore, we study the non-GRS properties of TGRS codes with two twists and prove that these codes are non-GRS in most cases.
Topics & Concepts
Reed–Solomon error correctionBlock codeReed–Muller codeLinear codeDual (grammatical number)Separable spaceDiscrete mathematicsComputer scienceCode (set theory)ArithmeticConcatenated error correction codeMathematicsAlgorithmDecoding methodsLinguisticsProgramming languagePhilosophyMathematical analysisSet (abstract data type)Coding theory and cryptographyCryptographic Implementations and SecurityError Correcting Code Techniques