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February  2007, 1(1): 45-64. doi: 10.3934/amc.2007.1.45

Double circulant codes from two class association schemes

Steven T. Dougherty 1, , Jon-Lark Kim 2, and  Patrick Solé 3,

1. 

Department of Mathematics, University of Scranton, Scranton, PA 18518, United States
2. 

Department of Mathematics, University of Louisville, Louisvile, KY 40292, United States
3. 

CNRS, I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia Antipolis, France

Received  April 2006 Revised  August 2006 Published  January 2007

Two class association schemes consist of either strongly regular graphs (SRG) or doubly regular tournaments (DRT). We construct self-dual codes from the adjacency matrices of these schemes. This generalizes the construction of Pless ternary Symmetry codes, Karlin binary Double Circulant codes, Calderbank and Sloane quaternary double circulant codes, and Gaborit Quadratic Double Circulant codes (QDC). As new examples SRG's give 4 (resp. 5) new Type I (resp. Type II) [72, 36, 12] codes. We construct a [200, 100, 12] Type II code invariant under the Higman-Sims group, a [200, 100, 16] Type II code invariant under the Hall-Janko group, and more generally self-dual binary codes attached to rank three groups.
Keywords: 2-class association scheme, doubly regular tournament., rank three groups, strongly regular graph, Self-dual code.
Mathematics Subject Classification: Primary: 94B60; Secondary: 05E3.
Citation: Steven T. Dougherty, Jon-Lark Kim, Patrick Solé. Double circulant codes from two class association schemes. Advances in Mathematics of Communications, 2007, 1 (1) : 45-64. doi: 10.3934/amc.2007.1.45
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