Browsing by Author "Douadi Mihoubi"

Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    CLASSIFICATION OF ELEMENTS IN ELLIPTIC CURVE OVER THE RING F
    (Université de M'sila, 2022) Bilel Selikh; Douadi Mihoubi
    Let Fq["] := Fq[X]/(X4 − X3) be a finite quotient ring where "4 = "3, with Fq is a finite field of order q such that q is a power of a prime number p greater than or equal to 5. In this work, we will study the elliptic curve over Fq["], "4 = "3 of characteristic p 6= 2, 3 given by homogeneous Weierstrass equation of the form Y 2Z = X3 + aXZ2 + bZ3 where a and b are parameters taken in Fq["]. Firstly, we study the arithmetic operation of this ring. In addition, we define the elliptic curve Ea,b(Fq["]) and we will show that E 0(a), 0(b)(Fq) and E 1(a), 1(b)(Fq) are two elliptic curves over the finite field Fq, such that 0 is a canonical projection and 1 is a sum projection of coordinate of element in Fq["]. Precisely, we give a classification of elements in elliptic curve over the finite ring Fq["].
  • Thumbnail Image
    ItemOpen Access
    Minimal and maximal cyclic codes of length 2p
    (2022) Lakhdar Heboub; Douadi Mihoubi
    In this paper, we compute the maximal and minimal codes of length 2p over finite fields q  with p and q are distinct odd primes and f( )= 1 p p − is the multiplicative order of q modulo 2p. We show that, every cyclic code is a direct sum of minimal cyclic codes