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Actively Secure OT-Extension from q-ary Linear Codes
cryptographic protocols oblivious transfer
2018/6/19
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...
Decoding Linear Codes with High Error Rate and its Impact for LPN Security
Decoding binary linear codes BJMM Nearest Neighbors
2017/11/28
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...
Linear codes with few weights from weakly regular bent functions based on a generic construction
Linear codes weight distribution p-ary functions
2015/12/21
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 ...
Asymptotically good binary linear codes with asymptotically good self-intersection spans
Asymptotically good binary linear codes asymptotically good self-intersection spans Information Theory
2012/4/16
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...
On the vanishing ideal of an algebraic toric set and its parameterized linear codes
algebraic toric set parameterized linear codes Commutative Algebra
2011/9/16
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...
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithm
Integer programming LP decoding Mathematical programming ML decoding Polyhedral theory
2011/9/14
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...
Local-Testability and Self-Correctability of q-ary Sparse Linear Codes
Local-Testability Self-Correctability q-ary Sparse Linear Codes
2011/3/3
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...
Information-set decoding for linear codes over Fq
Generalized McEliece cryptosystem security analysis Stern attack
2009/12/29
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...
Primal-dual distance bounds of linear codes with application to cryptography
Boolean function dual distance linear code minimum distance
2009/2/13
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 d⊥ is 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...
Weight Equations for Binary Linear Codes and Their Applications
Weight Equations Binary Linear Codes
2010/3/5
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.