Algebraic Decoding of Two Quadratic Residue Codes Using Unknown Syndrome Representation
نویسندگان
چکیده
This paper addresses the problem of improving the unknown syndrome representations to develop algebraic decoding of the (17,9,5) and (23,12,7) binary quadratic residue codes up to true minimum distance, respectively. The proposed unknown syndrome representations are expressed as binary polynomials in terms of the single known syndrome, which is different from the known syndrome in [Chang-Lee, Algebraic decoding of a class of binary cyclic codes via Lagrange interpolation formula, IEEE Trans. Inf. Theory, 2010]. Programs written in C++ language have been executed to obtain the optimal unknown syndrome representations for these two quadratic residue codes.
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