Math @ Duke

Publications [#235969] of Robert Calderbank
Papers Published
 Nastasescu, MM; Calderbank, AR, The projective Kerdock code,
2010 Ieee Information Theory Workshop
(August, 2010), IEEE [doi]
(last updated on 2019/04/21)
Abstract: Certain nonlinear binary codes can be constructed as binary images of Z4linear codes under the Gray map. Examples include the secondorder ReedMuller code and the Kerdock and Preparata codes. In this paper, we consider a new quaternary code which is an additive subcode of the Z 4linear Kerdock code. The Kerdock code is the direct sum of a onedimensional 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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