Constructing single-error-correcting codes using factorization of finite Abelian groups
Khalid Amin · International Journal of Algebra · 2014
Factorization of finite abelian groups was proposed by G. Hajos, when he was attempting to solve a conjecture about tiling by H. Minkowski. Hajos eventually settled this conjecture in its group-theoretic form. Subsequently, the notion of factorization of finite abelian groups was studied in the context of many other fields, ranging from number theory to geometry and coding theory. In this paper, we will use factorization of finite abelian groups to construct a single-error-correcting binary code of length seven and minimum hamming distance three.