Bounds for the Multicovering Radii of Reed-Muller Codes with Applications to Stream Ciphers

Authors:
I. Honkala;A. Klapper
Affiliations:
Dept. of Mathematics, University of Turku, 20014 Turku, Finland honkala@utu.fi;Dept. of Computer Science, 763H Anderson Hall, University of Kentucky, Lexington, KY 40506-0046 klapper@cs.uky.ed
Venue:
Designs, Codes and Cryptography
Year:
2001

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Abstract

The multicovering radii of a code are recentgeneralizations of the covering radius of a code. For positivem, the m-covering radius of C is the leastradius t such that everym-tuple of vectors is contained in at least one ball of radiust centered at some codeword. In this paper upper bounds arefound for the multicovering radii of first order Reed-Muller codes. These bounds generalize the well-known Norse bounds for the classicalcovering radii of first order Reed-Muller codes. They are exactin some cases. These bounds are then used to prove the existence of secure families of keystreams against a general class of cryptanalytic attacks. This solves the open question that gave rise to the study ofmulticovering radii of codes.