Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which
allows to store them efficiently. In this paper, we investigate it and prove some lower bounds …

Let F _q F q be a finite field with q elements, D_ 2n,\, r D 2 n, ra generalized dihedral group
with\gcd (2n, q)= 1 gcd (2 n, q)= 1, and F _q D_ 2n,\, r F q D 2 n, ra generalized dihedral …

Abstract Let D 2 n=< x, y∣ xn= 1, y 2= 1, yxy= x− 1> be a dihedral group, and R= GR (p 2, m)
be a Galois ring of characteristic p 2 and cardinality p 2 m where p is a prime. Left ideals of …

Let F q be a finite field with order q, Q 4 n the generalized quaternion group with 4 n
elements, and gcd (4 n, q)= 1. Firstly, central (right) irreducible idempotents of F q [Q 4 n] are …

Consider a finite field F q with characteristic p, where G is a crystallographic point group
satisfying p∤| G| and q= pn. In this paper, we propose studying group codes in the …

Let m be an arbitrary positive integer and D 8m be the dihedral group of order 8m, ie, D
8m=(x, y| x 4m= 1, y 2= 1, yxy= x-1). Left ideals of the dihedral group algebra F 2 [D 8m] are …

Let F q be the finite field of q elements and let D 2 n=< x, y| xn= 1, y 2= 1, yxy= xn− 1> be the
dihedral group of 2n elements. Left ideals of the group algebra F q [D 2 n] are known as left …

Let F q 2 be the finite field of q 2 elements, where q is a power of a prime number, and let D
2 n=< x, y| xn= 1, y 2= 1, yxy= xn− 1> be the dihedral group of 2n elements. Left ideals of the …

Let F _q F q be a finite field with order q and D 2 n be the dihedral group with 2 n elements,
and gcd (q, 2 n)= 1. In this article, the authors give precise descriptions and enumerations of …

We consider a special class of idempotent of semisimple group algebras which we call
essential. We give some criteria to decide when a primitive idempotent is essential; then we …