Binary Covering Arrays and Existentially Closed Graphs

  • Authors:
  • Charles J. Colbourn;Gerzson Kéri

  • Affiliations:
  • Computer Science and Engineering, Arizona State University, Tempe, U.S.A. AZ 85287;Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary H-1111

  • Venue:
  • IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
  • Year:
  • 2009

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Abstract

Binary covering arrays have been extensively studied in many different contexts, but the explicit construction of small binary covering arrays with strength larger than three remains poorly understood. Connections with existentially closed graphs and Hadamard matrices are examined, particularly those arising from the Paley graphs and tournaments. Computational results on arrays generated by column translation, such as the Paley graphs, lead to substantial improvements on known existence results for binary covering arrays of strengths four and five.