Coding, Cryptography and Combinatorics by Keqin Feng, Harald Niederreiter, Chaoping Xing

By Keqin Feng, Harald Niederreiter, Chaoping Xing

It has lengthy been famous that there are attention-grabbing connections among cod­ ing concept, cryptology, and combinatorics. as a result it appeared fascinating to us to prepare a convention that brings jointly specialists from those 3 components for a fruitful trade of rules. We selected a venue within the Huang Shan (Yellow Mountain) quarter, some of the most scenic parts of China, in an effort to give you the extra inducement of a beautiful position. The convention was once deliberate for June 2003 with the reliable identify Workshop on Coding, Cryptography and Combi­ natorics (CCC 2003). people who are acquainted with occasions in East Asia within the first half 2003 can bet what occurred finally, particularly the convention needed to be cancelled within the curiosity of the future health of the members. The SARS epidemic posed too critical a probability. on the time of the cancellation, the association of the convention used to be at a sophisticated degree: all invited audio system have been chosen and all abstracts of contributed talks have been screened via this system committee. therefore, it used to be de­ cided to name on all invited audio system and presenters of approved contributed talks to publish their manuscripts for booklet within the current quantity. Altogether, 39 submissions have been obtained and subjected to a different around of refereeing. After care­ ful scrutiny, 28 papers have been accredited for publication.

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Gm} be a chosen basis of [T]. 2) For id E Id Al/ A2 , let /-LAl/A2(id) or simply /-L(id) denote the coset leader of a coset whose id-number is id. 6) where infix "0" denotes the concatenation operation. We use the following notations. For a = /30,,( E {O,l}*, /3\a ~ "( and ah ~ /3. For /3,"( E {O,l}* and A ~ {a, l}*, /3\A ~ {/3\a: a E A} and Ah ~ {ah: a E A}. 8) 3. Parallel Concatenation Decomposition of Coset Sets In the original, top-down or adaptive RMLD, how to divide into sub-problems is specified by a binary sectionalization where each section is labelled 101 with index a E {O,l}*.

R. Blahut, editor. Kluwer Academic Publishers, 1994. [17] S. Leveiller, G. Zemor, P. Guillot and J. Boutros. A new cryptanalytic attack for PN-generators filtered by a Boolean function. Proceedings of Selected Areas of Cryptography 2002, LNCS 2595, pp. 232-249 (2003). J. J. Sloane. The Theory of Error-Correcting Codes, Amsterdam, North Holland, 1977. [19] S. Maitra and E. Pasalic. Further constructions of resilient Boolean functions with very high nonlinearity. IEEE Transactions on Information Theory, vol.

1,8] 10 = [1,4]' h = [5,8] loa = 1000 = [1,2]' 101 = [3,4]' .. [1, 1], 1001 = [2,2]' .. Levell Level 2 Level 3 1000 1001 1010 1011 1100 h01 1 110 hll Figure 1: The uniform binary section tree with N = 23 . RMLD is based on decomposition techniques. For a nonleaf section leo let A and B be a binary linear code and its linear subcode over 10:, respectively. 2) and if SbA = SbB for b E {O, I}, then there is a one-to-one correspondence between poA/soB and P1A/slB. For D E A/(soB 0 slB), PbD E PbA/SbB and the coset p/jD in p/jA/s/jB, where 0 ~ 1 and I ~ 0, (PbD,P/jD) is called an adjacent pair, and p/jD is called the counter part of PbD.

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