Construction of Association Scheme Using Some (123)-avoiding Class of Aunu Patterns

Abstract

5ABSTRACT: This paper presents some backgrounds research on association scheme using a class of (123)-avoiding pattern of Aunu numbers as an application area. It also attempts to highlight some further applications in other set structures. The finding in this research has shown that there is some interrelationship between the succession scheme used in generating Aunu numbers and the concept of association scheme. This research also shows us that the Aunu patterns can be used in design theory.

Combined Techniques of Hill Cipher and Transposition Cipher

“…Subsequently many research on transposition and substitution ciphers were conducted by different researchers such as [11], [13] and [15]. Many discussions on transposition and substitution ciphers were made [5], [7], [9], [12] and [17] evaluates the security of transposition ciphers using stack approaches, [1], [20] and [22] discusses a combination of two independent ciphers for a better securing of a data over a communication channels, [4], [6], [8] and [10] investigated enhancement of Ceaser cipher method, [15] discusses an approaches in improving transpositions cipher systems, [16] on modified Ceaser cipher for a better security situations, Azzam and [18] discusses a strong cipher text by combining Hill and Substitution Ciphers, and [14] on modification of an Affine ciphers algorithm for cryptography password. Cryptographic techniques uses two fundamental systems which are symmetric (secret key) and asymmetric (public key), in this study we use a symmetric key for both encryption and decryption.…”

“…(1 + (𝑝 − 1)𝑖)𝑚𝑝) where mp ≔ modulop. Many algebraic properties of 𝐆𝐩 were been investigated, and also cryptographic aspect of Gp were been investigated by [2] and [18].…”

Construction of B-Algebra on Cycles of Aunu Permutation Pattern

“…AUNU permutation pattern are a class of (123) and (132)-avoiding permutation pattern with special properties associated with succession schemes. These patterns have been used extensively in formulation of different structures such as group, graph and in study of different algebra schemes such as cyclic designs and circuit design see Mustapha and Ibrahim, (2013) ;Ibrahim, (20005); Magami et al, (2012). Some other theoretic properties of the AUNU Pattern and AUNU group were identify and discussed especially in relation to integer modulo group see Usman and Ibrahim, (2011).…”