De Bruijn cycles for covering codes

  • Authors:

  • Fan Chung;Joshua N. Cooper

  • Affiliations:

  • Department of Mathematics, University of California, San Diego, La Jolla, California 92093;Department of Mathematics, University of California, San Diego, La Jolla, California 92093 and Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 1 ...

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2004

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Abstract

A de Bruijn covering code is a q-ary string S so that every q-ary string is at most R symbol changes from some n-word appearing consecutively in S. We introduce these codes and prove that they can have size close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. Included is a table of the best known bounds on the lengths of small binary de Bruijn covering codes, up to R = 11 and n = 13, followed by several open questions in this area. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004