Add to ORKGWe define essential idempotents in group algebras and use them to prove that every mininmal abelian non-cyclic code is a repetition code. Also we use them to prove that every minimal abelian code is equivalent to a minimal cyclic code of the same length. Finally, we show that a binary cyclic code is simplex if and only if is of length of the form $n=2^k-1$ and is generated by an essential idempotent
2000 Mathematics Subject Classification: 94B05, 94B15.Cyclic binary codes C of block length n = 2^m ...
AbstractLet q be an odd prime power and p be an odd prime with gcd(p,q)=1. Let order of q modulo p b...
A finite group with a cyclic normal subgroup N such that G/N is cyclic is said to be metacyclic. A c...
We define essential idempotents in group algebras and use them to prove that every mininmal abelian ...
AbstractWe compute the number of simple components of a semisimple finite abelian group algebra and ...
AbstractIn this paper we show that two minimal codes M1 and M2 in the group algebra F2[G] have the s...
We study codes constructed from ideals in group algebras and we are particularly interested in their...
AbstractConstabelian codes can be viewed as ideals in twisted group algebras over finite fields. In ...
We study codes constructed from ideals in group algebras and we are particularly interested in their...
Given an integer m which is a product of distinct primes pi, a method is given for constructing code...
AbstractExplicit expressions for the (n+ 1) primitive idempotents inFG(the group algebra of the cycl...
Cyclic codes give us the most probable method by which we may detect and correct data transmission e...
In 1979, Miller proved that for a group $G$ of odd order, two minimal group codes in $\mathbb{F}_2G$...
AbstractIn this paper, some relations between the decompositions of codes and the groups of codes ar...
An algebra A is plain if it is nite, simple and has no non-trivial proper subalgebras. An element 0 ...
2000 Mathematics Subject Classification: 94B05, 94B15.Cyclic binary codes C of block length n = 2^m ...
AbstractLet q be an odd prime power and p be an odd prime with gcd(p,q)=1. Let order of q modulo p b...
A finite group with a cyclic normal subgroup N such that G/N is cyclic is said to be metacyclic. A c...
We define essential idempotents in group algebras and use them to prove that every mininmal abelian ...
AbstractWe compute the number of simple components of a semisimple finite abelian group algebra and ...
AbstractIn this paper we show that two minimal codes M1 and M2 in the group algebra F2[G] have the s...
We study codes constructed from ideals in group algebras and we are particularly interested in their...
AbstractConstabelian codes can be viewed as ideals in twisted group algebras over finite fields. In ...
We study codes constructed from ideals in group algebras and we are particularly interested in their...
Given an integer m which is a product of distinct primes pi, a method is given for constructing code...
AbstractExplicit expressions for the (n+ 1) primitive idempotents inFG(the group algebra of the cycl...
Cyclic codes give us the most probable method by which we may detect and correct data transmission e...
In 1979, Miller proved that for a group $G$ of odd order, two minimal group codes in $\mathbb{F}_2G$...
AbstractIn this paper, some relations between the decompositions of codes and the groups of codes ar...
An algebra A is plain if it is nite, simple and has no non-trivial proper subalgebras. An element 0 ...
2000 Mathematics Subject Classification: 94B05, 94B15.Cyclic binary codes C of block length n = 2^m ...
AbstractLet q be an odd prime power and p be an odd prime with gcd(p,q)=1. Let order of q modulo p b...
A finite group with a cyclic normal subgroup N such that G/N is cyclic is said to be metacyclic. A c...