Self-dual codes over GF(4)

Journal of Combinatorial Theory, Series A - Tập 25 Số 3 - Trang 288-318 - 1978
F. MacWilliams1, Andrew Odlyzko1, N. J. A. Sloane1, Harold N. Ward2
1Bell Laboratories Murray Hill, New Jersey 07974, USA
2University of Virginia, Charlottesville, Virginia 22901 USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Assmus, 1969, New 5-designs, J. Combinatorial Theory, 6, 122, 10.1016/S0021-9800(69)80115-8

Assmus, 1972, On weights in quadratic-residue codes, Discrete Math., 3, 1, 10.1016/0012-365X(72)90021-0

Assmus, 1974, Coding and combinatorics, SIAM Rev., 16, 349, 10.1137/1016056

Assmus, 1967, Research to develop the algebraic theory of codes, 10.21236/AD0656783

Bassalygo, 1974, Uniformly packed codes, Problems of Information Transmission, 10, 6

Broué, 1974, Codes correcteurs d'erreurs auto-orthogonaux sur le corps à deux éléments et formes quadratiques entiéres définies positives à discriminant + 1, 71

Broué, 1977, Discrete Math., 17, 247, 10.1016/0012-365X(77)90159-5

Broué, 1972, Polynômes des poids de certains codes et fonctions thêta de certains réseaux, Ann. Sci. École Norm. Sup., 5, 157, 10.24033/asens.1223

Brown, 1974

Conway, 1971, Groups, lattices, and quadratic forms, Vol. IV, 135

J. H. Conway and V. Pless, On the enumeration of self-dual codes, J. Combinatorial Theory, to appear.

Coxeter, 1965

Dembowski, 1968

Dickson, 1958

Dieudonné, 1971

Goethals, 1975, Uniformly packed codes, Philips Res. Rep., 30, 9

Hall, 1971, The ALTRAN system for rational function manipulation—a survey, Comm. ACM, 14, 517, 10.1145/362637.362644

W. C. Huffman, Polynomial invariants of finite linear groups of degree two, preprint.

MacWilliams, 1963, A theorem on the distribution of weights in a systematic code, Bell Syst. Tech. J., 42, 79, 10.1002/j.1538-7305.1963.tb04003.x

MacWilliams, 1969, Orthogonal matrices over finite fields, Amer. Math. Monthly, 76, 152, 10.2307/2317262

MacWilliams, 1971, Orthogonal circulant matrices over finite fields, and how to find them, J. Combinatorial Theory, 10, 1, 10.1016/0097-3165(71)90062-8

MacWilliams, 1972, Generalizations of Gleason's theorem on weight enumerators of self-dual codes, IEEE Trans. Information Theory, 18, 794, 10.1109/TIT.1972.1054898

MacWilliams, 1977

MacWilliams, 1972, Good self-dual codes exist, Discrete Math., 3, 153, 10.1016/0012-365X(72)90030-1

MacWilliams, 1973, On the existence of a projective plane of order 10, J. Combinatorial Theory, Ser. A, 14, 66, 10.1016/0097-3165(73)90064-2

Mallows, 1975, Upper bounds for modular forms, lattices, and codes, J. Algebra, 36, 68, 10.1016/0021-8693(75)90155-6

Mallows, 1976, Self-dual codes over GF(3), SIAM J. Appl. Math., 31, 649, 10.1137/0131058

Mallows, 1973, An upper bound for self-dual codes, Inform. Contr., 22, 188, 10.1016/S0019-9958(73)90273-8

1975, MACSYMA Reference Manual

Pless, 1972, A classification of self-orthogonal codes over GF(2), Discrete Math., 3, 209, 10.1016/0012-365X(72)90034-9

Pless, 1976, CAMAC, 171

Pless, 1975, On the classification and enumeration of self-dual codes, J. Combinational Theory, Ser. A, 18, 313, 10.1016/0097-3165(75)90042-4

Ritchie, 1974, The UNIX time-sharing system, Comm. ACM, 17, 365, 10.1145/361011.361061

Sloane, 1975, Weight enumerators of codes, 115

Sloane, 1977, Error-correcting codes and invariant theory: New applications of a nineteenth century technique, Amer. Math. Monthly, 84, 82, 10.2307/2319929

Thompson, 1976

Ward, 1976, A restriction on the weight enumerator of a self-dual code, J. Combinatorial Theory, Ser. A, 21, 253, 10.1016/0097-3165(76)90071-6

Sloane, 1979, Self-dual codes and lattices, 10.1090/pspum/034/525331