The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code

Author

Houghten, Sheridan K. ; Lam, Clement W H ; Thiel, Larry H. ; Parker, Jeff A.

Author_Institution

Dept. of Comput. Sci., Brock Univ., St. Catharines, Ont., Canada

Volume

49

Issue

1

fYear

2003

fDate

1/1/2003 12:00:00 AM

Firstpage

53

Lastpage

59

Abstract

An extremal self-dual doubly-even binary (n,k,d) code has a minimum weight d=4└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 three cases. A previous search assuming one of the cases found only the extended quadratic residue code. We examine the remaining two 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.

Keywords

Golay codes; binary codes; dual codes; residue codes; search problems; Golay code; complete search; extended quadratic residue code; extremal binary code; minimum code weight; self-dual doubly-even binary code; self-dual doubly-even code; Codes; Computer science; Councils; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2002.806146

Filename

1159761