Type II codes over double struck F sign2 m + u double struck F sign2 m

Abstract

We look at the special class of self-dual codes called Type II codes over the alphabet Rm = double struck F sign2 m + u double struck F sign2 m where u2 = 0. Properties of the Gray maps which take self-dual codes over Rm to self-dual codes over the subrings double struck F sign2 m and Rr = double struck F sign2 r + u double struck F sign2 r for divisors r of m are studied. We give a mass formula for Type II codes over Rm and classify such codes of length n≤8 for m = 2, 3, 4, 5, 6 and 7. © 2003 Elsevier B.V. All rights reserved.