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The triple-error-correcting binary Golay code has been used in DNA and communication systems. Recently, an algebraic decoding of the Golay code has been proposed by an unusual general error locator polynomials (GELP). This paper utilizes the interpolation method to obtain a new unusual GELP. Simulation results show that the Golay decoder using the presented unusual GELP significantly reduces the area...
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...
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