Self-dual codes over GF(7)

All maximal self-orthogonal and self-dual codes of length n where n\leq 9 are completely classified. A generator matrix, Hamming weight distribution, and order of the monomial group of each of these codes are given.

[1]  V. Pless.  On the uniqueness of the Golay codes , 1968 .

[2]  VLADIMIR D. TONCHEV.  Hadamard Matrices of Order 28 with Automorphisms of Order 13 , 1983, J. Comb. Theory, Ser. A.

[3]  Neil J. A. Sloane,et al.  Self-Dual Codes over ${\text{GF}}( 3 )$ , 1976 .

[4]  N. J. A. Sloane,et al.  Self-dual codes over GF(3) and GF(4) of length not exceeding 16 , 1979, IEEE Trans. Inf. Theory.

[5]  Vera Pless,et al.  A classification of self-orthogonal codes over GF(2) , 1972, Discret. Math..

[6]  N. J. A. Sloane,et al.  On the Classification and Enumeration of Self-Dual Codes , 1975, J. Comb. Theory, Ser. A.

[7]  N. J. A. Sloane,et al.  On ternary self-dual codes of length 24 , 1981, IEEE Trans. Inf. Theory.

[8]  Vera Pless.  The children of the (32, 16) doubly even codes , 1978, IEEE Trans. Inf. Theory.

[9]  N. J. A. Sloane,et al.  Self-Dual Codes over GF(4) , 1978, J. Comb. Theory, Ser. A.

[10]  N. J. A. Sloane,et al.  Self-Dual Codes over GF(5) , 1982, J. Comb. Theory, Ser. A.

[11]  Jeffrey S. Leon,et al.  Computing automorphism groups of error-correcting codes , 1982, IEEE Trans. Inf. Theory.

[12]  John H. Conway,et al.  On the Enumeration of Self-Dual Codes , 1980, J. Comb. Theory, Ser. A.