Title :
The minimum distance of the duals of binary irreducible cyclic codes
Author :
Ding, Cunsheng ; Helleseth, Tor ; Niederreiter, Harald ; Xing, Chaoping
Author_Institution :
Dept. of Comput. Sci., Hong Kong Univ. of Sci. & Technol., Kowloon, China
fDate :
10/1/2002 12:00:00 AM
Abstract :
Irreducible cyclic codes have been an interesting subject of study for many years. The weight distribution of some of them have been determined. We determine the minimum distance and certain weights of the duals of binary irreducible cyclic codes. We show that the weight distribution of these codes is determined by the cyclotomic numbers of certain order. As a byproduct, we describe a class of double-error correcting codes.
Keywords :
binary codes; cyclic codes; dual codes; error correction codes; Gaussian periods; Zetterberg codes; binary irreducible cyclic codes; cyclotomic numbers; double-error correcting codes; dual codes; minimum distance; weight distribution; Chaos; Codes; Computer science; Councils; Hamming weight; Informatics; Mathematics; Polynomials;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2002.802593
