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# Brock TR # CS-02-09 Abstract

*The Extended Quadratic Residue Code is the only (48, 24, 12) Self-Dual Doubly-Even Code * [PDF]

S.K. Houghten, C.W.H. Lam, L.H. Thiel, and J.A. Parker, May 2002.

The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4*floor(n/24) + 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous search assuming one of the cases found only the Extended Quadratic Residue Code. In this paper we examine the remaining 2 cases. Separate searches assuming each of the remaining cases found no codes and thus the Extended Quadratic Residue Code is the only doubly-even self-dual (48, 24, 12) code.