论文信息 - On the Automorphism Groups of Affine-Invariant Codes.

On the Automorphism Groups of Affine-Invariant Codes.

Using the classification of finite simple groups, we obtain a condition for a permutation group on a finite field GF(pm) to have the affine group AGL(1,pm) as a subgroup. Applying this result to the automorphism groups of non trivial affine-invariant codes, we prove that these automorphism groups are always subgroups of the general affine group AGL(m,p).

Thierry P. Berger | T. Berger

[1] J. Dieudonne,et al. On the automorphisms of the classical groups. With a supplement by Loo-Keng Hua , 1951 .

[2] R. Guralnick. Subgroups of prime power index in a simple group , 1983 .

[3] W. Knapp,et al. Codes with prescribed permutation group , 1980 .

[4] B. Huppert. Endliche Gruppen I , 1967 .

[5] Pascale Charpin. The Extended Reed-Solomon Codes Considered as Ideals or a Modular Algebra , 1983 .

[6] B. Huppert,et al. Finite Groups II , 1982 .

[7] Jean Alexandre Dieudonné,et al. On the automorphisms of the classical groups , 1951 .

[8] H. Wielandt,et al. Finite Permutation Groups , 1964 .

[9] B. Mortimer,et al. Permutation Groups Containing Affine Groups of the Same Degree , 1977 .

[10] G. Szekeres,et al. An inequality for the chromatic number of a graph , 1968 .

[11] F. MacWilliams,et al. The Theory of Error-Correcting Codes , 1977 .

[12] P. Cameron. FINITE PERMUTATION GROUPS AND FINITE SIMPLE GROUPS , 1981 .

[13] Noboru Ito. A characterization of quadratic residue codes , 1986 .

[14] W. Burnside,et al. Theory of Groups of Finite Order , 1909 .

[15] Thierry P. Berger. A direct proof for the automorphism group of Reed-Solomon codes , 1990, EUROCODE.

[16] Shu Lin,et al. Some Results on Cyclic Codes which Are Invariant under the Affine Group and Their Application , 1966, Inf. Control..