Plotkin construction: rank and kernel

Details Plotkin construction: rank and kernel Plotkin construction: rank and kernel

2007-07-26

arxiv.org/abs/0707.3878v1

Computer Science

Information Theory

Scientific paper

Given two binary codes of length n, using Plotkin construction we obtain a code of length 2n. The construction works for linear and nonlinear codes. For the linear case, it is straightforward to see that the dimension of the final code is the sum of the dimensions of the starting codes. For nonlinear codes, the rank and the dimension of the kernel are standard mesures of linearity. In this report, we prove that both parameters are also the sum of the corresponding ones of the starting codes.

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