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The binary self-dual codes of length up to 32: A revised enumeration. (English) Zbl 0751.94009
Summary: This paper presents a revised enumeration of the binary self-dual codes of length up to 32 given by {\it J. H. Conway} and {\it V. Pless} in 1978-1980. The list of 85 doubly-even self-dual codes of length 32 is essentially correct, but several of their descriptions need amending. The principal change is that there are 731 (not 664) inequivalent self-dual codes of length 30. Furthermore, there are three (not two) [28,14,6] and 13 (not eight) [30,15,6] self-dual codes. Some additional information is provided about the self-dual codes of length less than 32.

94B05General theory of linear codes
Full Text: DOI
[1] Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; Wilson, R. A.: ATLAS of finite groups. (1985) · Zbl 0568.20001
[2] Conway, J. H.; Pless, V.: On the enumeration of self-dual codes. J. combin. Theory ser. A 28, 26-53 (1980) · Zbl 0439.94011
[3] Conway, J. H.; Sloane, N. J. A: Sphere packings, lattices and groups. (1988) · Zbl 0634.52002
[4] Conway, J. H.; Sloane, N. J. A: A new upper bound on the minimal distance of self-dual codes. IEEE trans. Inform. theory 36, 1319-1333 (1990) · Zbl 0713.94016
[5] Curtis, R. T.: A new combinatorial approach to M24. Math. proc. Cambridge philos. Soc. 79, 25-42 (1976) · Zbl 0321.05018
[6] Koch, H. V.: On self-dual, doubly-even codes of length 32. Report P-math-32/84 (1984) · Zbl 0672.94008
[7] Macwilliams, F. J.; Sloane, N. J. A: The theory of error-correcting codes. (1977) · Zbl 0369.94008
[8] Mckay, B. D.: NAUTY user’s guide (Version 1.2). Dept. computer science technical report TR-CS-87-03 (1987)
[9] Pless, V.: A classification of self-orthogonal codes over $GF(2)$. Discrete math. 3, 209-246 (1972) · Zbl 0256.94015
[10] Pless, V.: The children of the (32, 16) doubly even codes. IEEE trans. Inform. theory 24, 738-746 (1978) · Zbl 0387.94010
[11] Pless, V.; Sloane, N. J. A: On the classification and enumeration of self-dual codes. J. combin. Theory ser. A 18, 313-335 (1975) · Zbl 0305.94011
[12] Yorgov, V. Y.: On the extremal doubly-even codes of length 32. Proceedings, fourth joint swedish-soviet international workshop on information theory, 275-279 (1989)