Gray isometries for finite chain rings and a nonlinear ternary (36, 3/sup 12/, 15) code

Abstract

Using tensor product constructions for the first-order generalized Reed-Muller codes, we extend the well-established concept of the Gray isometry between (Z/sub 4/, /spl delta//sub L/) and (Z/sub 2//sup 2/, /spl delta//sub H/) to the context of finite chain rings. Our approach covers previous results by Carlet (see ibid., vol.44, p.1543-7, 1998), Constantinescu (see Probl. Pered. Inform., vol.33, no.3, p.22-8, 1997 and Ph.D. dissertation, Tech. Univ. Munchen, Munchen, Germany, 1995), Nechaev et al. (see Proc. IEEE Int. Symp. Information Theory and its Applications, p.31-4, 1996) and overlaps with Heise et al. (see Proc. ACCT 6, Pskov, Russia, p.123-9, 1998) and Honold et al. (see Proc. ACCT 6, Pskov, Russia, p.135-41, 1998). Applying the Gray isometry on Z/sub 9/ we obtain a previously unknown nonlinear ternary (36, 3/sup 12/, 15) code.