The [72,36] Type II Self Dual Codes from Hadamard Matrices
Rowena T. Baylon-Cabrizos
Discipline: Statistics
Abstract:
Consider a code [n,k,d] of length n, dimension k and of minimum distance d. Let R be
a rate defined by the equation R = k/n. Mathematically, the main problem of coding
theory is to find codes with large R (for efficiency) and large d (to correct many errors).
This paper diseuses the binary [72,36] code constructed from Hadamard matrices.
References:
- Dougherty, S.T., T.A. Gulliver and M. Harada. 1997. External Binary Self Dual Codes. IEEE Trans. on Info. Theory. 43(6):2,036-2.
- Golay, M.J, E. 1949. Notes on Digital Coding. Proc. I.E.E.E. 37:657 A).
- Hamming, R. W. 1950. Error Detecting and Error Correcting Codes. Bell Syst. Tech. J. 29:147-160 (LA).
- MacWilliams, F.J_ 1963. A Theorem on the Distribution of Weights in a Systematic Code. Bell Syst. Tech. J. 42:79-94.
- MacWilliams, F.J., N.J.A. Sloane and J.G. Thompson. 1972. Good Self-Dual Codes Exist. Discrete Mathematics. 3.153-162.
- Mallows, C.L. and N.J-A- Sloane. 1973. An Upper Bound for Self-mal Codes. Info. and Control J. 22: 188-200.
- Ozeki, M. 1987. Hadamard Matrices and Doubly-Even Self-Dual Error Correcting Codes. J. of Combination Theory. A444:274-287.
- Shannon, C.E. 1948. A Mathematical Theory of Communication. Bell Syst. Tech. J. 27:379-423, 623-656.
- Sloane, NIA. 1972. Is There a (72,36) d 16 Self-mal Code? IEEE Trans. Info. Theory, IT-19:251.
- Tonchev, V.D. 1989. Self-Orthogonal Designs and External Doubly Even Codes J. of Combination Theory A (52): 197-205.
- Tonchev, V.D. and F.C. Bussemaker. 1990. External Doubly-Even Codes of Length 40 Derived from Hadamard Matrices of Order 20. Discrete Mathematics. 82: 317-321. www.uow.edu.au/-jennie/hadamard.html
ISSN 2984-7125 (Online)
ISSN 2244-4432 (Print)