2000 Mathematics Subject Classification: 94B05, 94B15.
Cyclic binary codes C of block length n = 2^m − 1 and generator polynomial g(x) = m1(x)m2^s+1(x), (s, m) = 1, are considered. The cardinalities of the sets of minimal codewords of weights 10 and 11 in codes C and of weight 12 in their extended codes
^C are determined. The weight distributions of minimal codewords in the binary Reed-Muller
codes RM (3, 6) and RM (3, 7) are determined. The applied method enables
codes with larger...
We describe an approach for recovering the plaintext in block ciphers having a design structure similar to the Data Encryption Standard but with improperly constructed S-boxes. The experiments with a backtracking search algorithm performing this kind of attack against modified DES/Triple-DES in ECB mode show that the unknown plaintext can be recovered with a small amount of uncertainty and this algorithm is highly efficient both in time and memory costs for plaintext sources with relatively low...
This work was presented in part at the 8th International Conference on Finite Fields and
Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.
In this paper, we study the ratio θ(n) = λ2 (n) / ψ2 (n), where λ2 (n) is
the number of primitive polynomials and ψ2 (n) is the number of irreducible
polynomials in GF (2)[x] of degree n. Let n = ∏ pi^ri, i=1,..l
be the prime factorization of n. We show that, for fixed l and ri , θ(n) is close to 1 and θ(2n) is
not less than 2/3 for sufficiently...
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