Journals Information
Universal Journal of Applied Mathematics Vol. 4(2), pp. 39 - 41
DOI: 10.13189/ujam.2016.040202
Reprint (PDF) (222Kb)
A Standard Generator/Parity Check Matrix for Codes from the Cayley Tables Due to the Non-associative (123)-Avoiding Patterns of AUNU Numbers
Ibrahim A.A 1, Chun P.B 2,*, Abubakar S.I 3, Garba A.I 1, Mustafa.A 1
1 Department of Mathematics, Usmanu Danfodiyo University Sokoto, Nigeria
2 Department of Mathematics, Plateau State University Bokkos, Nigeria
3 Department of Mathematics, Sokoto State University Sokoto, Nigeria
ABSTRACT
In this paper, we aim at utilizing the Cayley tables demonstrated by the Authors[1] in the construction of a Generator/Parity check Matrix in standard form for a Code say C Our goal is achieved first by converting the Cayley tables in [1] using Mod2 arithmetic into a Matrix with entries from the binary field. Echelon Row operations are then performed (carried out) on the matrix in line with existing algorithms and propositions to obtain a matrix say G whose rows spans C and a matrix say H whose rows spans C鈯�, the dual code of C, where G and H are given as, G = (Ik | X ) and H= ( -XT | In-k ). The report by Williem (2011) that the adjacency Matrix of a graph can be interpreted as the generator matrix of a Code [3] is in this context extended to the Cayley table which generates matrices from the permutations of points of the AUNU numbers of prime cardinality.
KEYWORDS
Carley Tables, AUNU Permutation Patterns, Generator Matrix, Parity Check Matrix, Standard Form, Pattern Avoidance, Echelon Row Operation, Non-associative, Non-commutative
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ibrahim A.A , Chun P.B , Abubakar S.I , Garba A.I , Mustafa.A , "A Standard Generator/Parity Check Matrix for Codes from the Cayley Tables Due to the Non-associative (123)-Avoiding Patterns of AUNU Numbers," Universal Journal of Applied Mathematics, Vol. 4, No. 2, pp. 39 - 41, 2016. DOI: 10.13189/ujam.2016.040202.
(b). APA Format:
Ibrahim A.A , Chun P.B , Abubakar S.I , Garba A.I , Mustafa.A (2016). A Standard Generator/Parity Check Matrix for Codes from the Cayley Tables Due to the Non-associative (123)-Avoiding Patterns of AUNU Numbers. Universal Journal of Applied Mathematics, 4(2), 39 - 41. DOI: 10.13189/ujam.2016.040202.