THE WEIGHT HIERARCHY OF HADAMARD CODES.

The support of an (n,M, d) binary code C over the set A = {0, 1} is the set of all coordinate positions i, such that at least two codewords of C have distinct entry in coordinate i. If C is a code of size M, then r-th generalized Hamming weight, dr(C), 1 ≤ r ≤ 1+log2(M -1), of C is defined as the minimum of the cardinalities of the supports of all subset of C of cardinality 2r-1 + 1. The sequence (d1(C), d2(C), . . ., dk(C)) is called the Hamming weight hierarchy (HWH) of C. In this paper we obtain HWH for (2k-1, 2k, 2k-1) binary Hadamard code corresponding to Sylvester Hadamard matrix H2k and we show that dr = 2k-r(2r - 1). Also we compute the HWH of (4n - 1, 4n, 2n) Hadamard codes for 2 ≤ n ≤ 8. [ABSTRACT FROM AUTHOR]