Title :
Optimal Cyclic Codes With Generalized Niho-Type Zeros and the Weight Distribution
Author :
Maosheng Xiong ; Nian Li
Author_Institution :
Dept. of Math., Hong Kong Univ. of Sci. & Technol., Hong Kong, China
Abstract :
In this paper, we extend two earlier works further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are optimal and have only a few non-zero weights. Besides using similar ideas, we carry out some subtle manipulation of certain exponential sums.
Keywords :
cyclic codes; polynomials; exponential sums; generalized Niho-type zeros; generator polynomial; optimal cyclic codes; parity-check polynomial; weight distribution; Additives; Electronic mail; Hamming weight; Indexes; Linear codes; Polynomials; Standards; Cyclic codes; Niho exponent; Vandermonde matrix; weight distribution;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2015.2451657
