Open AccessClass of repeated‐single‐root cyclic codes for power‐line communications
Author(s) -
Rocha V.C.
Publication year - 2016
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/el.2016.1877
Subject(s) - codebook , mathematics , hamming distance , combinatorics , hamming code , prime power , dimension (graph theory) , discrete mathematics , line (geometry) , prime (order theory) , root (linguistics) , hamming weight , block code , algorithm , decoding methods , linguistics , philosophy , geometry
A class of p ‐ary ( n , k , d ) cyclic codes with block length n = p , dimension k = 2 and minimum Hamming distance d = n − k + 1 = p − 1 is introduced, where p denotes a prime. These codes are maximum distance separable repeated‐single‐root cyclic codes with generator polynomial g ( x ) = ( x ‒1) p ‒2 . The codebook has size p 2 and contains a subset of p ( p ‒ 1)codewords having p distinct symbols each. The size of is maximum for the given parameters and its codewords are useful for applications of coded modulation in power‐line communications.