On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions

Finite Fields and Their Applications - Tập 14 Số 1 - Trang 22-40 - 2008
Hai Q. Dinh1
1Department of Mathematical Sciences, Kent State University, 4314 Mahoning Avenue, Warren, OH 44483, USA

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Tài liệu tham khảo

Berlekamp, 1968, Negacyclic Codes for the Lee Metric, 298

Berlekamp, 1984

Castagnoli, 1991, On repeated-root cyclic codes, IEEE Trans. Inform. Theory, 37, 337, 10.1109/18.75249

Delsarte, 1972, Bounds for unrestricted codes, by linear programing, Philips Res. Rep., 27, 272

Delsarte, 1973, Four fundamental characters of a code and their combinatorial significance, Inform. Control, 23, 407, 10.1016/S0019-9958(73)80007-5

Delsarte, 1973, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl., 10

Dinh, 2005, Negacyclic codes of length 2s over Galois rings, IEEE Trans. Inform. Theory, 51, 4252, 10.1109/TIT.2005.859284

Dinh, 2007, Complete distances of all negacyclic codes of length 2s over Z2a, IEEE Trans. Inform. Theory, 53, 147, 10.1109/TIT.2006.887487

Dinh, 2004, Cyclic and negacyclic codes over finite chain rings, IEEE Trans. Inform. Theory, 50, 1728, 10.1109/TIT.2004.831789

Huffman, 2003

Krawtchouk, 1929, Sur une généralisation des polynomes d'Hermite, C. R. Acad. Sci. Paris, 189, 620

Krawtchouk, 1933, Sur la distribution des racines des polynomes orthogonaux, C. R. Acad. Sci. Paris, 196, 739

MacWilliams, 1961, Error-correcting codes for multiple-level transmissions, Bell System Tech. J., 40, 281, 10.1002/j.1538-7305.1961.tb03986.x

F.J. MacWilliams, Combinatorial problems of elementary abelian groups, PhD Diss., Harvard University, Cambridge, MA, 1962

MacWilliams, 1998

McDonald, 1974, Finite Rings with Identity, vol. 28

Nedeloaia, 2003, Weight distributions of cyclic self-dual codes, IEEE Trans. Inform. Theory, 49, 1582, 10.1109/TIT.2003.811921

Pless, 1998

E. Prange, Cyclic error-correcting codes in two symbols, technical notes, TN-57-103, Air Force Cambridge Research Labs, Bedford, MA, September 1957

E. Prange, Some cyclic error-correcting codes with simple decoding algorithms, TN-58-156, Air Force Cambridge Research Labs, Bedford, MA, April 1958

E. Prange, The use of coset equivalence in the analysis and decoding of group codes, TN-59-16, Air Force Cambridge Research Labs, Bedford, MA, 1959

E. Prange, An algorithm for factoring xn−1 over a finite field, TN-59-175, Air Force Cambridge Research Labs, Bedford, MA, October 1959

Szegő, 1959, Orthogonal Polynomials, vol. 23

Tang, 1997, A note on the q-ary image of a qm-ary repeated-root cyclic code, IEEE Trans. Inform. Theory, 43, 732, 10.1109/18.556131

van Lint, 1991, Repeated-root cyclic codes, IEEE Trans. Inform. Theory, 37, 343, 10.1109/18.75250