The design of totally self-checking checkers for some classes of Hadamard codes

Hadamard codes are derived from the rows of Hadamard matrices, and are widely used in signal processing, feature extractions, communications, and so forth. In this paper, the designs of totally self-checking checkers for these codes are considered. On account of their property that total number of codewords are small and their patterns are limited, same extra ideas are required to establish self-testing properties. There are 3 kinds of Hadamard matrices, Sylvester type, M sequence type and Paley type. The checker design obtained here is applicable to Paley type matrices of degree 8m+4, where m is a nonnegative integer, by making use of the property of difference sets. In the case of matrices of degree 8m+8, the checker design is still an open question. It is also shown that Sylvester type and M sequence type Hadamard codes checkers are obtained by systematic code checker design. Therefore, the total results obtained here cover the majority of Hadamard codes known so far.