An Algebraic Approach for Decoding Spread Codes

In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires O((n-k)k^3) operations over an extension field F_{q^k}. Our algorithm is more efficient than the previous ones in the literature, when the dimension k of the codewords is small with respect to n. The decoding algorithm takes advantage of the algebraic structure of the code, and it uses original results on minors of a matrix and on the factorization of polynomials over finite fields

Amide-controlled, one-pot synthesis of tri-substituted purines generates structural diversity and analogues with trypanocidal activity

Anovel one-pot synthesis of tri-substituted purines and the discovery of purine analogues with trypanocidal activity are reported. The reaction is initiated by a metal-free oxidative coupling of primary alkoxides and diaminopyrimidines with Schiff base formation and subsequent annulation in the presence of large N,N-dimethylamides (e.g.N,N-dimethylpropanamide or larger). This synthetic route is in competition with a reaction previously-reported by our group1, allowing the generation of a combinatorial library of tri-substituted purines by the simple modification of the amide and the alkoxide employed. Among the variety of structures generated, two purine analogues displayed trypanocidal activity against the protozoan parasite Trypanosoma brucei with IC50 , 5 mM, being each of those compounds obtained through each of the synthetic pathways.J.J.D.M. thanks Spanish Ministerio de Economı´a y Competitividad for a Ramon y Cajal Fellowship. A.U.B. thanks MRC IGMM for an academic fellowship. This work was partially supported by Grant SAF2011-30528 to J.A.G.S.

Polynomial Time Attack on Wild McEliece Over Quadratic Extensions

International audienceWe present a polynomial time structural attack against the McEliece system based on Wild Goppa codes from a quadratic finite field extension. This attack uses the fact that such codes can be distinguished from random codes to compute some filtration of nested subcodes which will reveal their secret algebraic description

Code based cryptography and steganography

Abstract. For a long time, coding theory was only concerned by message integrity (how to protect against errors a message sent via some noisely channel). Nowadays, coding theory plays an important role in the area of cryptography and steganography. The aim of this paper is to show how algebraic coding theory offers ways to define secure cryptographic primitives and efficient steganographic schemes. Cryptography