New Extremal Self-dual Codes of Length 36

Djoko Suprijanto ( Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)
Bagus Ilman ( Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)

Jurnal Matematika & Sains
Vol 15, No 3 (2010)

A paper of Conway and Sloane (1990) gives the putative weight enumerators of extremal self-dual codes for length n £ 64 and n = 72. The construction of such codes with putative weight enumerator has been one of the fundamental problems in Coding Theory. In this paper, we construct new extremal binary self-dual codes of length 36. We show that there are at least 17 inequivalent extremal binary self-dual codes of parameter  [36, 18, 8]. Our invention upgrades the previous known result provided by Conway and Sloane (1990), Harada (1999), and Kim (2001).