New Codes Beyond the Zyablov Bound and the Goppa-Based Justesen Codes.

摘要

In this report, constructions are given for two new block codes. The first construction produces a class of asymptotically good codes that lie above both the Zyablov and SKHN bounds for certain rates. The counting techniques of Weldon are discussed and generalized and are used to compute a lower-bound on the distance-to-length ratio of the new codes. The codes themselves are constructed by concatenating an SKHN code (due to Sugiyama, et al.) with an interleaved code generated by a fixed (no, kO, dO) base code having weight enumerator WO(x). The second construction produces a class of codes J sub G which lies on the Justesen bound. These codes arise from the concatenation of a maximum distance separable code with a set of Goppa Codes. If a sufficiently large number of Goppa Codes are used as inner codes, we produce a class J sub G codes that lie on the Justesen bound for all rates.