مؤسسة الشرق الأوسط للنشر العلمي
عادةً ما يتم الرد في غضون خمس دقائق
The aim of this study is to find theories that show the relationship between the perfect linear code and the Hamming codes, as we study the possibility that each Hamming bound is a perfect code, as well as every binary code is a perfect. We will study new examples in coding theory that prove these theories. In these examples, we found the generator matrix G of a [m, p]-code ∁ and the codedwords, weight distribution of ∁ and then we found the minimum (Hamming) distance d. Such that we get a code ∁ that achieves the relationship, if q ^ (m -p)>∑ _ (i = 0) ^ (d - 2)((m - 1 @ i)) (q - 1) ^ i , then there always exists a [m, p, d] - q- code.