Spherical Codes And Set Partitioning On The Real Line

Abstract

New constructions of spherical codes in Euclidean n-spaces are suggested. [3] T. Ericson and V. Zinoviev, Concatenated spherical presented at the Eurocode 90, Udine Italy, November 5-9,1990. Set partitioning is a fundamental principle for the construction of codes for non-Hamming metrics. The idea is closely related to the idea of generalized code concatenation. Following the work of Ungerboeck there has recently been a great interest in this idea for construction of codes in Euclidean spaces. Ungerboeck's coding scheme can be viewed as a concatenation using convolutional codes for the outer encoding. In the present paper we investigate concatenations using block codes as outer codes. Several new principles are introduced. The point-sets under consideration are equally spaced points on the real line. The outer codes are various combinations of binary codes, involving both linear and constant weight codes. The results we have include: i)