We derive a simple formula to generate a wide-sense systematic generator matrixBfor a Reed-Solomon code. Specifically, we generate the generator matrixBsuch that the columns with indices ¿1, ¿2,..., ¿kare the columns of the identity matrixIk. One possible application of these wide-sense matrices is erasures-only decoding.

Narrowband interference can cause undetected errors when M-FSK data is encoded with an algebraic code containing the all-ecodewords. This is due to the fact that the narrowband interferer will cause the output of the M-FSK demodulator to correspond to one of the all-ecodewords. One possible solution is to use a coset code of a code containing the repetition code. The choice of the coset leader should be such that the resulting coset code has minimum same-symbol weight. We give a general construction for generating coset codes with minimum same-symbol weight and present results where an optimal coset code for an (n, k) Reed-Solomon code is applied in an M-FSK environment with narrowband interference. From the results it is evident that the optimal coset codes outperform linear codes when narrowband interference is present.