More on the unified unknown syndrome representations for a class of binary cyclic codes

The unified unknown syndrome representation has recently been developed to decode a class of binary cyclic codes. Each unknown syndrome is expressed as a sparse and binary polynomial in terms of the single syndrome, and the degrees of nonzero terms in the binary polynomial satisfy one congruence relation. This paper utilizes the properties of finite fields to interpolate extra points such that more binary polynomials for the unknown syndrome are generated. Two decoding examples of the (17, 9, 5) and (43, 29, 6) binary cyclic codes are given.