Algorithms for Extended Galois Field Generation and Calculation

Zhaneta Savova-Tasheva, Antoniya Tasheva

Abstract


The paper aims to suggest algorithms for Extended Galois Field generation and calculation. The algorithm analysis shows that the proposed algorithm for finding primitive polynomial is faster than traditional polynomial search and when table operations in GF(pm) are used the algorithms are faster than traditional polynomial addition and subtraction.

Keywords


Extended Galois Field; GF(p); GF(p^m); Primitive Polynomials

Full Text:

PDF

References


E.R. Berlekamp, Algebraic coding theory. McGraw-Hill, 1968.

G. Birkhoff, S. Mac Lane, A survey of modern algebra. Universities Press, 1965.

R.C. Bose, D.K. Ray-Chaudhuri, On a class of error correcting binary group codes, Information control, 3, (1960) 279-290.

C.G. Clark Jr., J.B. Cain, Error-correction coding for digital communications, Springer Science & Business Media, 2013.

Y. Li, H. Wang, J. Zhao, On the Primitivity of some Trinomials over Finite Fields. IACR Cryptology ePrint Archive 2013 (2013): 252.

R. Lidl, H. Niederreiter, Finite fields, Vol. 20, Cambridge university press, 1997.

J.L. Massey, Coding theory, In W. Lederman and S. Vajda, editors, Handbook of Applicable Mathematics, Vol. 5, Combinatorics and Geometry, Chichester and New York: Wiley, (1985) 623-676.

J.L. Massey, O. N. Garcia, Error-correcting codes in computer arithmetic, In J. Tou, editor, Advances in Information Systems Science, Vol. 4, New York: Plenum Press, (1972) 273-326.

J.L. Massey, Some applications of coding theory in cryptography. In P. G. Farrell, editor, Codes and Cyphers: Cryptography and Coding IV, Essex, England, Formara Ltd. (1995) 33-47.

W.W. Peterson, E.J. Weldon, Error-correcting codes. MIT press, 1972.

I.S. Reed, G. Solomon, Polynomial codes over certain finite fields, J Soc. Ind. Appl. Match, 8, (1960) 300-304.


Refbacks

  • There are currently no refbacks.