Since the proof in 1982, by Tsfasman VlÌ† aduÅ£ and Zink of the existence of algebraic-geometric (AG) codes with asymptotic performance exceeding the Gilbertâ€“Varshamov (Gâ€“V) bound, one of theâ€¦ (More)

ANY GOOD CODES over GF(q) can be constructed as subfield subcodes of codes that are defined M over some bigger field GF( q"), e.g., BCH-codes, for i = l ; . . , n } . Goppa codes and theirâ€¦ (More)

A major problem in coding theory is the question if the class of cyclic codes is asymptotically good. In this paper we introduce-as a generalization of cyclic codes-the notion of transitive codesâ€¦ (More)

Applicable Algebra in Engineering, Communicationâ€¦

2002

We present a simple construction of long linear codes from shorter ones. Our approach is related to the product code construction; it generalizes and simplifies substantially the recent â€œPropagationâ€¦ (More)

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Iharaâ€™sâ€¦ (More)

We discuss some recent constructions of codes from algebraic curves due to Xing, Niederreiter, and Lam, and we investigate their relations with Goppaâ€™s algebraic-geometric codes.

The Gilbert-Varshamov (GV) bound for asymptotic families of codes over F/sub q/ has been improved by Tsfasman, Vla/spl breve/dut$80, and Zink (TVZ) in 1982, and only recently further improvementsâ€¦ (More)

Abstracf-The weight hierarchy of a linear code is the set of generalized Hamming weights of the code. In this paper, we consider geometric Goppa codes and provide a lower bound on their generalizedâ€¦ (More)