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We consider recent constructions of 11-out-of-NN OT-extension from Kolesnikov and Kumaresan (CRYPTO 2013) and from Orrú et al. (CT-RSA 2017), based on binary error-correcting codes. We generalize thei...
Technically, our improvement comes from the heavy use of Nearest Neighbor techniques in all steps of the construction, whereas the BJMM-algorithm can only take advantage of Nearest Neighbor search in ...
Given a linear code C, one can define the d-th power of C as the span of all componentwise products of d elements of C. A power of C may quickly fill the whole space. Our purpose is to answer the foll...
We contribute to the knowledge of linear codes with few weights from special polynomials and functions. Substantial efforts (especially due to C. Ding) have been directed towards their study in the ...
If C is a binary linear code, let C^2 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for C ranging...
Abstract: Let K be a finite field and let X be a subset of a projective space, over the field K, which is parameterized by monomials arising from the edges of a clutter. We show some estimates for the...
Abstract: Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iter...
We prove that q-ary sparse codes with small bias are self-correctable and locally testable. We generalize a result of Kaufman and Sudan [3] that proves the local testability and correctability of bina...
A code-based cryptosystem is considered secure if the best known attack against it is information-set decoding. Stern’s algorithm and its improvements are well optimized and the complexity is reason...
Let N(d, d⊥) denote the minimum length n of a linear code C with d and d⊥, where d is the minimum Hamming distance of C and dis the minimum Hamming distance of C⊥. In this paper, we show a lower ...
The system of weight equations for a binary (n, m)-code with respect to its ordered basis is introduced. It connects certain quantities (characteristics) related to the basis with the weights of non-z...
Some combinatorial problems concerning binary vector spaces are solved by applying the techniques developed in [1]. These illustrate that they are effective tools for such purposes.

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