TY - GEN

T1 - The projective Kerdock code

AU - Nastasescu, Maria Monica

AU - Calderbank, A. R.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - 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.

AB - 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.

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U2 - 10.1109/CIG.2010.5592761

DO - 10.1109/CIG.2010.5592761

M3 - Conference contribution

AN - SCOPUS:80051937674

SN - 9781424482641

T3 - 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

BT - 2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings

T2 - 2010 IEEE Information Theory Workshop, ITW 2010

Y2 - 30 August 2010 through 3 September 2010

ER -