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A Construction of Matrices with No Singular Square Submatrices

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

Abstract

This paper presents a new construction of matrices with no singular square submatrix. This construction allows designing erasure codes over finite field with fast encoding and decoding algorithms.

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References

  1. McWilliams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North Holland, Amsterdam (1977)

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  2. Rizzo, L.: Effective erasure codes for reliable computer communication protocols. ACM Computer Communication Review (April 1997)

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  3. Bloemer, J., Kalfane, M., Karpinski, M., Karp, R., Luby, M., Zuckerman, D.: An XOR-Based Erasure-Resilient Coding Scheme, ICSI TR-95-048 (August 1995)

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  4. Shparlinski: On singularity of Generalized Vandermonde Matrices Over Finite Fields (submitted for publication)

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  5. Gohberg, I., Olshevsky, V.: Fast Algorithms with preprocessing for matrix-vector multipication problems. Journal of Complexity 10 (1994)

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© 2004 Springer-Verlag Berlin Heidelberg

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Lacan, J., Fimes, J. (2004). A Construction of Matrices with No Singular Square Submatrices. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_11

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

  • eBook Packages: Springer Book Archive

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