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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| Published in | IEEE transactions on information theory Vol. 46; no. 7; pp. 2628 - 2633 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.11.2000
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | 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. |
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| AbstractList | 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. In this correspondence, we explain how to construct Goppa codes, expurgated or extended Goppa codes invariant under a permutation induced by an element of the projective semilinear group P Gamma L (2, GF (p super(m))). This follows 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 (cf. [6]). Moreover, it is easy to construct quasi-cyclic Goppa or related codes. Often, we obtain parameters unknown for quasi-cyclic codes (cf. [8]). 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 Gamma L(2, GF (p super(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 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 PGammaL(2, GF (p(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 In this correspondence, we explain how to construct Goppa codes, expurgated or extended Goppa codes invariant under a permutation induced by an element of the projective semilinear group PGammaL(2, GF(Pm). |
| Author | Berger, T.P. |
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| References | ref13 ref12 skersys (ref15) 1999 brouwer (ref6) 1998; 1 ref2 ref1 ref17 ref16 macwilliams (ref11) 1986 mceliece (ref10) 1978 ref4 chen (ref8) 2000 ref3 canteaut (ref7) 1998 dür dur (ref9) 1987; 4 sendrier (ref14) 1999 bosma (ref5) 1994 |
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| Snippet | We explain how to construct Goppa codes, expurgated or extruded Goppa codes invariant under a permutation induced by an element of the projective semilinear... In this correspondence, we explain how to construct Goppa codes, expurgated or extended Goppa codes invariant under a permutation induced by an element of the... |
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| SubjectTerms | Automorphisms Codes Coding Computer programming Construction Extrusion Goppa codes Handbooks Invariants Permutations Tables (data) |
| Title | Goppa and related codes invariant under a prescribed permutation |
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