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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...
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.