EXTENDED EUCLIDEAN ALGORITHM OF AUNU BINARY POLYNOMIALS OF CARDINALITY ELEVEN

Abstract

Binary polynomials representation of Aunu permutation patterns has been used to perform arithmetic operations on words and sub-words of the polynomials using addition, multiplication, and division modulo two. The polynomials were also found to form some mathematical structures such as group, ring, and field. This paper presents the extension of our earlier work as it reports the Aunu binary polynomials of cardinality eleven and how to find their greatest common divisor (gcd) using the extended Euclidean algorithm. The polynomials are pairly permuted and the results found showed that one polynomial is a factor of the other polynomial or one polynomial is relatively prime to the other and some gave different results. This important feature is of combinatorial significance and can be investigated further to formulate some theoretic axioms for this class of Aunu permutation pattern. Binary polynomials have important applications in coding theory, circuit design, and the construction of cryptographic primitives.