Goppa and related codes invariant under a prescribed permutation

We explain how to construct Goppa codes, expurgated or extruded Goppa codes invariant under a permutation induced by an element of the projective semilinear group P/spl Gamma/L(2, GF (p/sup m/)). This follows from the knowledge of semilinear automorphism groups of generalized Reed-Solomon codes. We...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 46; no. 7; pp. 2628 - 2633
Main Author Berger, T.P.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.11.2000
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Automorphisms
Codes
Coding
Computer programming
Construction
Extrusion
Goppa codes
Handbooks
Invariants
Permutations
Tables (data)
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Summary:We explain how to construct Goppa codes, expurgated or extruded Goppa codes invariant under a permutation induced by an element of the projective semilinear group P/spl Gamma/L(2, GF (p/sup m/)). This follows from the knowledge of semilinear automorphism groups of generalized Reed-Solomon codes. We obtain very good codes: some of them have parameters which reach the values given in the Brouwer table (see Handbook of Coding Theory, V.S. Pless and W.C. Huffman, Eds. Amsterdam, The Netherlands: Elsevier, vol.1, ch.4., 1998).. Moreover, it is easy to construct quasi-cyclic Goppa or related codes. Often, we obtain parameters unknown for quasi-cyclic codes.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0018-9448
1557-9654
DOI:10.1109/18.887871