Type II codes over F4+uF4
Date of Issue2001
School of Physical and Mathematical Sciences
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  and . 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  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.
European journal of combinatorics
© 2001 Academic Press. This is the author created version of a work that has been peer reviewed and accepted for publication by European Journal of Combinatorics, Academic Press. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1006/eujc.2001.0509].