Author(s)： Michio Ozeki

J. Math-for-Ind. 1B (2009) 105-121.

• File： JMI2009B-4.pdf (175KB)

Abstract
H. Koch [7], [8] derived formulas which describe design structure supported by the codewords of fixed weight in the extremal binary self-dual doubly even codes. His method uses the lattices (not extremal lattices) constructed from such codes and the modular forms associated with these lattices. The formulas imply the so called Assmus-Mattson theorem for binary codes as partial results plus an extra formula which is not obtainable from the original Assmus-Mattson theorem.

In the present paper we develop a similar method to derive the formulas for the ternary self-dual extremal codes. The method also uses the lattice theory and the modular form theory. However in using the lattice theory the present paper differes largely from the ones by Koch.

Keyword(s).　 ternary extremal code, design equation