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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.

MSC:
94B05General theory of linear codes
Software:
nauty
WorldCat.org
Full Text: DOI
References:
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[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)