2017/08/23 by Tapabrata Roy, Roy, Tapabrata, Santanu Sarkar +1
Computer Science · Engineering · #Coding theory and cryptography #Cellular Automata and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1708.06913
In this paper we study ∏i=1n ℤ2i-Additive Cyclic Codes. These codes are identified as ℤ2n[x]-submodules of ∏i=1nℤ2i[x]/ ⟨ xαi-1⟩; αi and \rmi being relatively prime for each i=1,2,…,n. We first define a ∏i=1nℤ2i-additive cyclic code of a certain length. We then define the distance between two codewords and the minimum distance of such a code. Moreover we relate these to binary codes using the generalized Gray maps. We define the duals of such codes and show that the dual of a ∏i=1nℤ2i-additive cyclic code is also cyclic. We then give the polynomial definition of a ∏i=1nℤ2i-additive cyclic code of a certain length. We then determine the structure of such codes and derive a minimal spanning set for that. We also determine the total number of codewords in this code. We finally give an illustrative example of a ∏i=1nℤ2i-additive cyclic code.