ERROR DETECTION AND CORRECTION OF THE [15 8 3]-PERFECT CODE DUE TO THE AUNU AVOIDING PERMUTATION PATTERNS
Pamson B. Chun, N. Jeltel, Kamoh N.M, S. Abah · Universal Journal of Mathematics and Mathematical Sciences · 2024
The error correction and detection of the (7 4) Hamming code and other codes of smaller lengths are demonstrated using Venn diagrams. Alon and Liu [1] about two decades ago demonstrated how a binary block code of length $\ell \geq 3$ and $n$ being the greatest integer such that $2^n-1 \leq \ell$ can be encoded and decoded using the concept of the power set. In their approach, the word length has been chosen to be the greatest integer $m$ such that $m<2^n-\binom{\tilde{n}}{0}-\binom{\tilde{n}}{1}$. They tried to generalize it on a set of $n$ elements satisfying $2^n-1 \leq \ell$. In this paper, we adopt their approach by enumerating it on the [15 8 3]perfect code constructed earlier by the authors. Our demonstration shows clearly that their approach is a suitable alternative error detection and correction scheme for this code and other binary codes satisfying these conditions. Received: December 15, 2023;Revised: March 28, 2024;Accepted: April 14, 2024