### Journals Information

**
Computer Science and Information Technology Vol. 4(2), pp. 45 - 47 DOI: 10.13189/csit.2016.040201 Reprint (PDF) (219Kb) **

## Algebraic Theoretic Properties of the Non-associative Class of (132)-Avoiding Patterns of AUNU Permutations: Applications in the Generation and Analysis of a General Cyclic Code

**Chun P. B ^{1}^{,*}, Ibrahim A.A ^{2}, Garba A.I ^{2}**

^{1}Department of Mathematics, Plateau State University, Nigeria

^{2}Department of Mathematics, Usmanu Danfodiyo University, Nigeria

**ABSTRACT**

The author had in [1] and based on the report as in [2], established interplay between the adjacency matrices due to Eulerian graphs constructed by the application of AUNU numbers and the generation and analysis of a general linear code. That was achieved by constructing a [5 3 2] -linear code C of size M=8. This paper reviews such a construction of a linear code as in [1] extending the approach to a larger (linear cyclic) code which is a supper code say C^{1} of the [5 3 2]-linear code C of size M=8, ie C⊆ C^{1}. To achieve this, the generator matrix G as in [1] that generated C is further developed to give a matrix say G^{1} which now spans a larger linear code C^{1} of length n=5, dimension K=4 and size M=32. This is attainable by exhausting the cyclic shifts in the rows of the matrix G to give G^{1}. It is then shown through some existing remarks and proven theorems that the linear code generated by G^{1} is cyclic and has generator polynomial g(x)=1+x.

**KEYWORDS**

AUNU Numbers, Non-associative Class of AUNU Patterns, Linear Codes, Cyclic Shifts, Cyclic Codes, Generator Polynomials, Irreducible Polynomials, Generator Matrix

**Cite this paper**

Chun P. B , Ibrahim A.A , Garba A.I (2016). Algebraic Theoretic Properties of the Non-associative Class of (132)-Avoiding Patterns of AUNU Permutations: Applications in the Generation and Analysis of a General Cyclic Code. *Computer Science and Information Technology, 4 , * 45 - 47. doi: 10.13189/csit.2016.040201.