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Designs, Codes and Cryptography

, Volume 9, Issue 2, pp 177–191 | Cite as

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

  • Ron M. Roth
Article
  • 31 Downloads

Abstract

Codes \({\mathcal{C}}(m,r)\) of length 2 m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of \({\mathcal{C}}(m,r)\) all have an rth order spectral null at zero frequency. Establishing the connection between \({\mathcal{C}}(m,r)\) and the parity-check matrix of Reed-Muller codes, the minimum distance of \({\mathcal{C}}(m,r)\) is obtained along with upper bounds on the redundancy of \({\mathcal{C}}(m,r)\). An efficient algorithm is presented for encoding unconstrained binary sequences into \({\mathcal{C}}(m,r)\).

Hadamard matrices Reed-Muller codes Spectral-null codes 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Ron M. Roth
    • 1
  1. 1.Computer Science DepartmentTechnion—Israel Institute of TechnologyHaifaIsrael

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