Decoding RS Codes And Investigating Dimensions Of SSRS Codes

The decoding algorithms for RS codes are the most important thing in practical applications. On account of minimum distance, this paper proposes two cases for the decoding algorithms for RS codes. Particularly, the paper analyzes the number of errors for correcting on list decoding algorithm and extended list decoding algorithm for RS codes, and studies how to choice parameters such that the algorithm can correct more errors by the conditions of polynomial. Then we give the greatest number of errors for correcting on a list decoding algorithm and a extended list decoding algorithm. These are very useful for correcting on account of the practical applications to choice parameters.In this paper, we will extend some conclusions about the dimension of the SSRS codes. We study the structures and the calculations of the SSRS codes over the finite field GF(qm)(q is a power of a prime p). Then we give a formula for the dimension of a SSRS code. From the analyses of the formula, a sufficient and necessary condition as well as an algorithm is given under which we can judge whether a vector is a code word of SSRS code. We also analyze the lower bound of the dimension of and the parameters when the dimension of SSRS code is minimized. In addition, the subspace (ordinary subspace) is analyzed when the dimension of SSRS code is minimized. And we get some relations among the subspace, the trace-dual subspace and the corresponding cyclotomic matrix.Finally, the most important thing for the dimension of a SSRS code is the power of the components in the base of the trace-dual subspace. It's very useful for the study of identifying high-dimension.