7 research outputs found
On the minimum number of minimal codewords
We study the minimum number of minimal codewords in linear codes from the
point of view of projective geometry. We derive bounds and in some cases
determine the exact values. We also present an extension to minimal subcode
supports.Comment: 8 pages, 1 tabl
Weight distribution of a class of cyclic codes of length
Let be a finite field with elements and be a positive integer. In this paper, we determine the weight distribution of a class cyclic codes of length over whose parity check polynomials are either binomials or trinomials with zeros over , where integer . In addition, constant weight and two-weight linear codes are constructed when
A geometric characterization of minimal codes and their asymptotic performance
In this paper, we give a geometric characterization of minimal linear codes.
In particular, we relate minimal linear codes to cutting blocking sets,
introduced in a recent paper by Bonini and Borello. Using this
characterization, we derive some bounds on the length and the distance of
minimal codes, according to their dimension and the underlying field size.
Furthermore, we show that the family of minimal codes is asymptotically good.
Finally, we provide some geometrical constructions of minimal codes.Comment: 22 page
Secret-sharing with a class of ternary codes
Theoretical Computer Science2461-2285-298TCSC