2018/02/28 by Yuan Cao, Cao, Yuan, Yonglin Cao +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1803.00467
openalex publication_date 2018/02/28 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
Let R=ℤ4[v]/⟨ v2+2v⟩=ℤ4+vℤ4 (v2=2v) and n be an odd positive integer. Then R is a local non-principal ideal ring of 16 elements and there is a ℤ4-linear Gray map from R onto ℤ42 which preserves Lee distance and orthogonality. First, a canonical form decomposition and the structure for any negacyclic code over R of length 2n are presented. From this decomposition, a complete classification of all these codes is obtained. Then the cardinality and the dual code for each of these codes are given, and self-dual negacyclic codes over R of length 2n are presented. Moreover, all 23⋅(4p+5⋅ 2p+9)^\frac2p-2p negacyclic codes over R of length 2Mp and all 3⋅(4p+5⋅ 2p+9)^\frac2p-1-1p self-dual codes among them are presented precisely, where Mp=2p-1 is a Mersenne prime. Finally, 36 new and good self-dual 2-quasi-twisted linear codes over ℤ4 with basic parameters (28,228, dL=8,dE=12) and of type 21447 and basic parameters (28,228, dL=6,dE=12) and of type 21646 which are Gray images of self-dual negacyclic codes over R of length 14 are listed.