Open AccessThe Hamming Distances of a Class of p ‐Ary Negacyclic Codes
Author(s) -
DING Jian,
LI Hongju
Publication year - 2018
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2017.10.001
Subject(s) - hamming distance , hamming code , combinatorics , mathematics , hamming graph , hamming bound , upper and lower bounds , minimum distance , hamming(7,4) , discrete mathematics , algorithm , block code , mathematical analysis , decoding methods
Based on the construction of a new distance‐preserving Gray map from (( F p + uF p ) N , Gray distance) to (the corresponding Gray images in F pN p , Hamming distance) and the calculation of Gray distances of ( u −1)‐constacyclic codes over F p + uF p , a bound for the Hamming distances of a class of negacyclic codes with length pN over F p is obtained, which is more tighter than Singleton bound. Further more, the exact Hamming distances of some p ‐ary negacyclic codes are determined from this bound, some of which cannot be got from Dinh's work published on Finite Fields and Their Applications in 2008.