Showing papers on "Goppa code published in 1978"
IBM1
TL;DR: Irreducible Goppa codes extended with an overall parity check are shown to be cyclic or shortened cyclic codes and the location points of a codeword of the extended irreducibles codes can be designated as thepoints of a finite projective geometry.
Abstract: Irreducible Goppa codes extended with an overall parity check are shown to be cyclic or shortened cyclic codes. The location points of a codeword of the extended irreducible codes can be designated as the points of a finite projective geometry. Bounds on the number of equivalence classes of both irreducible and extended irreducible Goppa codes are derived.
22 citations
TL;DR: In a previous correspondence, a decoding procedure which uses continued fractions and which is applicable to a wide class of algebraic codes including Goppa codes was presented, the efficiency of this method is significantly increased.
Abstract: In a previous correspondence, a decoding procedure which uses continued fractions and which is applicable to a wide class of algebraic codes including Goppa codes was presented The efficiency of this method is significantly increased
4 citations
01 Jan 1978
TL;DR: This investigation determines some relationships between the class of generalized Coppa codes described by Tzeng and Zitnmeraann and cyclic codes.
Abstract: This investigation determines some relationships between the class of generalized Coppa codes described by Tzeng and Zitnmeraann and cyclic codes A new form of the parity-check matrix for generalized Goppa Codes is described, which lends itself to this type of investigation. It is shown that of the class of generalized Goppa Codes with the location set L an entire field and g(z) having no repeated roots, the only codes that can be extended to be cyclic are the subclass of Goppa Codes with g(z) a quadratic polynomial. For the class of generalTO A ized Goppa Codes with L GF(q ) (8) and g(z) (Z-B) it is shown that the subclass of codes with P(z) [L'(z)] , where b is an integer relative prime to q -1 and a any positive integer, is cyclic. Some results are presented for the class of generalized Goppa Codes with L = GF(q) { Bj_ . B2 > and &(z) " (z-Bj) (z-B2> ■ y are 2 (1) that the subclass of codes with P(z) k/(z-8o) . where k is any element of an extension field of GF(q ), can be extended to be cyclic by appending an overall parity check. (2) that the subclass of codes with P(z) k(z-Bi) 2 /(z-B?) with k as above can be extended to be eye lie. (3) that the subclass of codes with P(z) k( zt1 ) / ( z? 2) can be extended to be cyclic Finally, some related problems for further investigation have been suggested. CHAPTER