Document Type : Research Paper
Author
DEPT. OF INFORMATION SYSTEMS -COLLEGE OF COMPUTERS -UNIVESITY OF AL-ANBAR
Abstract
A polynomial p(x)= a + a x + …+ a x is said to be a permutation polynomial over a finite ring R If P permute the elements of R . where R is the ring ( Z , + , ) . It is known that mutually orthogonal Latin of order n,where n is the element in Z generate A [ ] – error correcting code with n code words . And we found no a pair of polynomial defining a pair of orthogonal Latin square modulo Z where n = 2 generate a linear code.
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[1] Marshall Hall, Jr. Combinatorial Theory. Blaisdell publishing company , 1967 .
[2] G.H. Hardy and E. M. Wright. An Introduction to the theory of Numbers,Oxford Clarendon Press , fourth edition , 1983 .
[3] Rudolf Lidl and Gary L. Mullen. When dose a polynomial over a finite field permute the elements of the field ? The American Math. Monthly, 95 (3) : 243- 246 , Mar 1988 .
[4] Rex Matthews. Permutation properties of the polynomial 1+ x + … + x over a finite field . Proc. Amer. Math. Soc., 120(1):47-51. Jan 1994 .
[5] G. Mullen and H. S tevens . Polynomial function (mod m ) . Acta Mathematica Hungaria, 44(3-4):237-241 , 1984 .
[6] Joachim von Gathen. Tests for permutation polynomials . SIAM J. Computing, 20(3) : 591-602, June 1991 .
[7] J.Denes and A.D. Keedwell , Latin square and their applications , A cademic Press , New York and London , ( 1974 ) .
[8] John B. Fraleigh , A First Course in Abstract Algebra , Addison – Wwsley , Massachusetts , (1997) .
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