Proje tions of Binary Linear Codes onto Larger Fields

Projections of Binary Linear Codes onto Larger Fields

We study certain projections of binary linear codes onto larger fields. These projections include the well-known projection of the extended Golay [24, 12, 8] code onto the Hexacode over GF(4) and the projection of the Reed-Muller code R(2, 5) onto the unique self-dual [8, 4, 4] code over GF(4). We give a characterization of these projections, and we construct several binary linear codes which h...

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...

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...

Mining for High Dimensional Clusters using Proje tions and Visualizations

Reverse Engineering of Network Software Binary Codes for Identification of Syntax and Semantics of Protocol Messages

Reverse engineering of network applications especially from the security point of view is of high importance and interest. Many network applications use proprietary protocols which specifications are not publicly available. Reverse engineering of such applications could provide us with vital information to understand their embedded unknown protocols. This could facilitate many tasks including d...