Weight Distributions of the Cosets of the (32,6) Reed-Muller Code

IEEE Transactions on Information Theory

Volumn 18, Issue 1, 1972, Pages 203-207

  Berlekamp, Elwyn R ^a   Welch, Lloyd R ^b  

^a Department of Electrical Engineering and Computer Science and the Departrnent of Mathematics sity of California ^*  (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

REED-MULLER CODES;

INFORMATION THEORY;

EID: 0015288079     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1972.1054732     Document Type: Article

References (10)

1. E. R. Berlekamp, Algebraic Coding Theory. New York: McGraw-Hill, 1968.
2. —, “Some mathematical properties of a scheme for reducing the bandwidth of motion pictures by Hadamard smearing,” Bell Syst. Tech. J., vol. 49, 1970, pp. 969–986.
3. T. Kasami, N. Tokura, and S. Azumi, “On the weight distribution of Reed-Muller codes” (in Japanese), Faculty Elec. Eng., Osaka Univ., Osaka, Japan, 1971.
4. N. J. A. Sloane and E. R. Berlekamp, “Weight enumerator for second-order Reed-Muller codes,” IEEE Trans. Inform. Theory, vol. IT-16, Nov. 1970, pp. 745-751.
5. T. Kasami and N. Tokura, “On the weight structure of Reed-Muller codes,” IEEE Trans. Inform. Theory, vol. IT-16, Nov. 1970, pp, 752–7 5 9.
6. R. J. Lechner, “Theory of switching,” Ph.D. dissertation, Comput. Lab., Harvard Univ., Boston, Mass., 1963; also Bell Telephone Lab., Murray Hill, N.J., Rep, BL-33, p. 4-4.
7. R. J. McEliece, “Linear recurring sequences over finite fields,” Ph.D. dissertation, Dep, Math., California Inst. Technol., Pasadena, 1967.
8. E. C. Posner, “Combinatorial structures and planetary recon-naissance,” in Error-Correcting Codes, H. B. Mann, Ed. New York: Wiley, 1968.
9. M. Sugino, Y. Ienaga, N. Tokura, and T. Kasami, “Weight distribution of (128,64) Reed-Muller code,” IEEE Trans. Inform. Theory (Corresp.), vol. IT-17, Sept. 1971, pp. 627-628.
10. R. J. Dick and N. J. Sloane, “Enumeration of cosets of first-order Reed-Muller codes,” to be published.