Integer codes have been successfully applied to various areas of communication and computer technology. They demonstrate good performance in correcting specific kinds errors. In many cases, the used integer are constructed by search. This paper presents an algebraic construction over ring integers modulo A=2n+1 capable at least up two bit errors a single b-byte. Moreover, can correct some confi...

In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number p = 2 − 1, where n is a prime, a positive integer h , and two n -bit integers T,R , find two n -bit integers F,G each of Hamming weight at most h such that T = F ·R+G modulo p , under the promise that they exist.

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

Let p > 3 be a prime, ζp a pth primitive root of 1, and ∆ the Galois group of Q(ζp) over Q. Let q 6= p be a prime and n the order of q modulo p. Assume q 6≡ 1 mod p and so n ≥ 2, p(q− 1)|qn − 1, and n|p− 1. Set f = (q − 1)/p and e = (p− 1)/n. Let Q be a prime ideal of Z[ζp] above q and let F = Z[ζp]/Q. Thus F ∼= Fqn , the finite field with q elements. Let α ∈ Z[ζp] be a generator of F such that...