Superimposed concatenated codes (Corresp.)

A family of codes of length n=q^{s+l} over GF( q ), with 2s \leq q are presented which are constructed by superimposing concatenated codes on a concatenated code. The rate r and the distance ratio \delta of the new codes satisfy the relation r=1-\delta+\delta \ln (\delta) for sufficiently large values of n and q/s . The new codes are superior to the comparable Bose-Chaudhuri-Hocquenghem (BCH) codes, for s\geq 3 , in the sense that they contain more codewords. An asymptotically good code constructed using these new codes has a distance ratio greater than those of other asymptotically good codes known to the authors for rates smaller than 0.007.