We recover the first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs via a covering argument. It is possible to sh...
The order bound for the minimum distance of algebraic geometry codes is defined for the dual of one-point codes. A new bound for the minimum distance of linear codes, and for codes...
Olav Geil, Carlos Munuera, Diego Ruano, Fernando T...
Fix positive integers B and w. Let C be a linear code over F2 of length Bw. The 2-regular-decoding problem is to find a nonzero codeword consisting of w length-B blocks, each of w...
Daniel J. Bernstein, Tanja Lange, Christiane Peter...
Abstract—This paper generalizes the classical Knuth–Schönhage algorithm computing the greatest common divisor (gcd) of two polynomials for solving arbitrary linear Diophantine...
We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes...