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Title: Construction of Hadamard Z2Z4Q8-codes
Author: Montolio Aranda, Pere
Tutor: Rifà Coma, Josep
Others: Universitat Oberta de Catalunya
Keywords: Hadamard codes
Issue Date: Feb-2014
Publisher: Universitat Oberta de Catalunya
Abstract: This work deals with Hadamard Z2Z4Q8-codes, which are binary codes after a Gray map from a subgroup of the direct product of Z2, Z4 and Q8 groups, where Q8 is the non-commutative quaternion group. These kind of codes have five types ("shapes") and the values or range of values of several characteristic parameters is analyzed. Specifically, we show that all these codes can be represented in a standard form from a set of generators, as well as using the parameters of dimension of the kernel and rank. In addition, we present several methods that allow, given some preselected values of these parameters, the construction of Hadamard Z2Z4Q8-codes fulfilling them.
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