On structured trellises of some best [n,k,d] codes

The paper presents two important new results. The first result is that it is possible to construct linear binary block codes with codeword length, n, number of information symbols in codewords, k, and code distance, d, which reach the upper or lower bounds on maximal code-distance, using the construction of M. Kasahara et al. (see IEEE Trans. on Inform. Theory, vol.IT-22, p.462-8, 1976) for some combination of the mentioned parameters. The second is a method of how to find a structured trellis of the code obtained via the above construction. The practical importance for wireless communications is that knowledge of the structured trellis can allow decoding of the corresponding code using different soft (turbo) algorithms. In this way, the set of useful codes for practical applications is broadened to ´best´ codes, that would otherwise be difficult to decode using soft algorithms.