The projective Kerdock code

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Nastasescu, MM; Calderbank, AR

Published Date

  • December 1, 2010

Published In

  • 2010 Ieee Information Theory Workshop, Itw 2010 Proceedings

Digital Object Identifier (DOI)

  • 10.1109/CIG.2010.5592761

Citation Source

  • Scopus