A new class of Fibonacci sequence based error correcting codes

Abstract

A new class of matrices is introduced for use in error control coding. This extends previous results on the class of Fibonacci error correcting codes. For a given integer p, a (p+1)×(p+1) binary matrix Mp is given whose nonzero entries are located either on the superdiagonal or the last row of the matrix. The matrices Mpn${M^{n}_{p}}$ and Mp?n$M^{-n}_{p}$, the nth power of Mp and its inverse, are employed as the encoding and decoding matrices, respectively. It is shown that for sufficiently large n, independent of the message matrix M, relations exist among the elements of the encoded matrix E=M×Mpn$E=M\times {M_{p}^{n}}$. These relations play a key role in the error detection and correction.