Annals of Combinatorics 1 (1997) 279-295
Studies on the Squaring Construction
Kristian Wahlgren and Zhe-Xian Wan
Department of Information Technology, Information Theory Group, Lund
University P.O. Box 118, S-221 00 Lund, Sweden
Received June 20, 1997
AMS Subject Classification: 05B40, 11H31, 94B75
Abstract. The code formulas for the iterated squaring construction
for a finite group partition chain, derived by Forney , are extended
to the case with a bi-infinite group partition chain, and the derivation
presented here is much simpler than the one given by Forney for the finite
case. It is also proven that the iterated squaring construction indeed
generates the Reed-Muller codes. Moreover, the generalization of the code
formulas to the bi-infinite case is used to derive code formulas for the
lattices Λ (r,n) and R Λ (r,n),
which correct some errors in .
Keywords: lattice, squaring construction, Reed-Muller codes, Barnes-Wall lattice
1. G.D. Forney, Jr., Coset codes - Part I: introduction and geometrical classification, IEEE Trans. Inform. Theory 34 (1988) 1123–1151.
2. G.D. Forney, Jr., Coset codes - Part II: binary lattices and related codes, IEEE Trans. Inform. Theory 34 (1988) 1152–1187.
3. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam et al., 1977.