Construction and Classification of Generalized Hadamard Codes over Eisenstein Local Rings
The research paper examines the design principles and structural features of Generalized Hadamard (GH) codes that operate within Eisenstein local rings Z2sw, utilizing a primitive cube root of unity ω that fulfils w2+w+1=0. The paper first introduces an algebraic Eisenstein integer framework before developing appropriate Gray mapping to examine binary-domain representations of these codes. We establish the essential criteria and necessary checks for determining the linear properties of GH codes based on Z2sw structures. This research work defines the kernel structure of these codes together with their rank specification and structural properties evaluation. A classification system for Z2sw-linear Hadamard codes presents itself in the last part according to their algebraic and combinatorial characteristics. Future studies about coding techniques within algebraic integer rings can begin from our current work because our research expands the understanding of code theory on non-traditional rings.
The Schafer-Wayne equation (SWE), a crucial model for ultrashort pulse propagation in nonlinear silicon optical fibers, is investigated using the F-expansion method and enhanced modified extended…
This paper presents a multiple RGB image encryption scheme that utilizes a pair of 8 x 8 S-boxes constructed over the residue classes of Eisenstein integers ZΩπ, implemented…
The research paper examines the design principles and structural features of Generalized Hadamard (GH) codes that operate within Eisenstein local rings Z2sw,…