Projections of Binary Linear Codes onto Larger Fields

Proje tions of Binary Linear Codes onto Larger Fields

Linear codes with complementary duals related to the complement of the Higman-Sims graph

‎In this paper we study codes $C_p(overline{{rm HiS}})$ where $p =3,7‎, ‎11$ defined by the 3‎- ‎7‎- ‎and 11-modular representations of the simple sporadic group ${rm HS}$ of Higman and Sims of degree 100‎. ‎With exception of $p=11$ the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over $GF(3)$ and $GF(7).$ We show that these codes ha...

DISCRETE TOMOGRAPHY AND FUZZY INTEGER PROGRAMMING

We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.

New binary and ternary LCD codes

LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield-subcodes of $J$-affine variety codes are a generalization of B...

Reed-Muller codes: Projections onto GF (4) and multilevel construction

A projection of binary Reed–Muller codes ( ) onto GF (4) is presented. For an ( ) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed–Muller ( 1 2) code. Based upon this projection, multilevel construction is given for ( ), where the constituent codes applied to the different levels are themselves the Reed–Muller codes ( 2 2) an...