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Bounds for the Multicovering Radii of ReedMuller Codes with Applications to Stream Ciphers
, 1999
"... The multicovering radii of a code are recent generalizations of the covering radius of a code. For positive m, the mcovering radius of C is the least radius t such that every mtuple of vectors is contained in at least one ball of radius t centered at some codeword. In this paper upper bounds are ..."
Abstract

Cited by 3 (1 self)
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The multicovering radii of a code are recent generalizations of the covering radius of a code. For positive m, the mcovering radius of C is the least radius t such that every mtuple of vectors is contained in at least one ball of radius t centered at some codeword. In this paper upper bounds are found for the multicovering radii of first order ReedMuller codes. These bounds generalize the wellknown Norse bounds for the classical covering radii of first order ReedMuller codes. They are exact in 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 of multicovering radii of codes.
ON THE PROPERTIES AND COMPLEXITY OF
, 2005
"... People rely on the ability to transmit information over channels of communication that are subject to noise and interference. This makes the ability to detect and recover from errors extremely important. Coding theory addresses this need for reliability. A fundamental question of coding theory is wh ..."
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People rely on the ability to transmit information over channels of communication that are subject to noise and interference. This makes the ability to detect and recover from errors extremely important. Coding theory addresses this need for reliability. A fundamental question of coding theory is whether and how we can correct the errors in a message that has been subjected to interference. One answer comes from structures known as error correcting codes. A well studied parameter associated with a code is its covering radius. The covering radius of a code is the smallest radius such that every vector in the Hamming space of the code is contained in a ball of that radius centered around some codeword. Covering radius relates to an important decoding strategy known as nearest neighbor decoding. The multicovering radius is a generalization of the covering radius that was proposed by Klapper [11] in the course of studying stream ciphers. In this work we develop techniques for finding the multicovering radius of specific codes. In particular, we study the even weight code, the 2error correcting BCH code, and linear codes with covering radius one. We also study questions involving the complexity of finding the multicovering radius of
Quasigroups in cryptology
, 2009
"... We give a review of some known published applications of quasigroups in cryptology. ..."
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We give a review of some known published applications of quasigroups in cryptology.