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Decoding Perfect Maps

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Abstract

Perfect Maps are two-dimensional arrays in which every possible sub-array of a certain size occurs exactly once. They are a generalization of the de Bruijn sequences to two dimensions and are of practical significance in certain position location applications. In such applications the decoding problem, i.e., resolving the position of a particular sub-array within a specified Perfect Map, is of great significance. In this paper new constructions for (binary) Perfect Maps and 2k-ary de Bruijn sequences are presented. These construction methods, although not yielding Perfect Maps for new sets of parameters, are significant because the Maps they yield can be efficiently decoded.

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Authors and Affiliations

  1. Computer Science Department, Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, Surrey, England

    Chris J. Mitchell

  2. Mathematics Department, University of London, Royal Holloway, London, England

    Kenneth G. Paterson

Authors
  1. Chris J. Mitchell
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  2. Kenneth G. Paterson
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Additional information

Communicated by D. Jungnickel

Funded by SERC CASE award No. 90C/11574.

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Mitchell, C.J., Paterson, K.G. Decoding Perfect Maps. Des Codes Crypt 4, 11–30 (1994). https://doi.org/10.1007/BF01388557

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  • DOI: https://doi.org/10.1007/BF01388557

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