Type II codes over F4+uF4

Abstract

Self-dual codes over F4 for the Euclidean scalar product [2, 6] and over F2 + uF2 [1, 5] received some attention lately. In the present article, we study codes over an alphabet R of size 16 that contains both alphabets as subrings. As a consequence, we obtain via suitable Gray maps self-dual codes over these two subrings which, in turn, give self-dual binary codes by the Gray maps of [6] and [5]. In particular, we introduce a subclass (Type II codes) of these self-dual codes over R which yield, after double Gray mapping, doubly even binary codes.Following a trend illustrated in [1] we also give constructions of lattices; specifically Z-lattices, Gaussian lattices and lattices over the golden integers via Construction A. A connection with Tits quaternionic construction of the Leech lattice [4, 8] is pointed out.