Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something which can be called a descent algebra. For any Coxeter group that is also a Weyl group, Paola Cellini proved the existence of a different, commutative subalgebra of...

In this paper, Reed Solomon (RS) decoder adopting the pipelined reduced inversion free Berlekamp Massey (pRiBM) algorithm is proposed. This Reed Solomon decoder is designed by equipping the Syndrome Computation unit, Key Equation Solver (KES), Chien search and Forney algorithm unit. The RS decoder requires long latency for decoding large number of test vectors. Therefore, the Reed Solomon decod...

In this paper we investigate the structure of quasi-BCH codes. In the first part of this paper we show that quasi-BCH codes can be derived from Reed-Solomon codes over square matrices extending the known relation about classical BCH and Reed-Solomon codes. This allows us to adapt the Welch-Berlekamp algorithm to quasi-BCH codes. In the second part of this paper we show that quasi-BCH codes can ...