Title :
Studying the locator polynomials of minimum weight codewords of BCH codes
Author :
Augot, Daniel ; Charpin, Pascale ; Sendrier, Nicolas
Author_Institution :
Lab. d´´Inf. Theor. et Programmation, Paris Univ., France
fDate :
5/1/1992 12:00:00 AM
Abstract :
Primitive binary cyclic codes of length n=2m are considered. A BCH code with designed distance δ is denoted B(n,δ). A BCH code is always a narrow-sense BCH code. A codeword is identified with its locator polynomial, whose coefficients are the symmetric functions of the locators. The definition of the code by its zeros-set involves some properties for the power sums of the locators. Moreover, the symmetric functions and the power sums of the locators are related to Newton´s identities. An algebraic point of view is presented in order to prove or disprove the existence of words of a given weight in a code. The principal result is the true minimum distance of some BCH codes of length 255 and 511. which were not known. The minimum weight codewords of the codes B(n2h -1) are studied. It is proved that the set of the minimum weight codewords of the BCH code B(n,2m-2-1) equals the set of the minimum weight codewords of the punctured Reed-Muller code of length n and order 2, for any m
Keywords :
error correction codes; polynomials; BCH codes; Newton´s identities; locator polynomials; minimum weight codewords; power sums; primitive binary cyclic codes; symmetric functions; true minimum distance; Galois fields; Information theory;
Journal_Title :
Information Theory, IEEE Transactions on