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The projective Kerdock code

Publication ,  Journal Article
Nastasescu, MM; Calderbank, AR
Published in: 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings
December 1, 2010

Certain nonlinear binary codes can be constructed as binary images of Z4-linear codes under the Gray map. Examples include the second-order Reed-Muller code and the Kerdock and Preparata codes. In this paper, we consider a new quaternary code which is an additive subcode of the Z 4-linear Kerdock code. The Kerdock code is the direct sum of a one-dimensional quaternary code and the quaternary subcode examined in this paper. This paper calculates the weight distribution of the projective Kerdock code from which the weight distribution of the dual code can be computed. The dual code is a supercode of the quaternary Preparata code. The projective Kerdock code is used to construct a deterministic measurement matrix for compressed sensing. Numerical experiments are presented for sparse reconstruction using the LASSO that show improvement over random Gaussian matrices of the same size. © 2010 IEEE.

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2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

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Publication Date

December 1, 2010
 

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Nastasescu, M. M., & Calderbank, A. R. (2010). The projective Kerdock code. 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings. https://doi.org/10.1109/CIG.2010.5592761
Nastasescu, M. M., and A. R. Calderbank. “The projective Kerdock code.” 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings, December 1, 2010. https://doi.org/10.1109/CIG.2010.5592761.
Nastasescu MM, Calderbank AR. The projective Kerdock code. 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings. 2010 Dec 1;
Nastasescu, M. M., and A. R. Calderbank. “The projective Kerdock code.” 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings, Dec. 2010. Scopus, doi:10.1109/CIG.2010.5592761.
Nastasescu MM, Calderbank AR. The projective Kerdock code. 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings. 2010 Dec 1;

Published In

2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

DOI

Publication Date

December 1, 2010