Hyperplane Sections of Fermat Varieties in P3 in Char.2 and Some Applications to Cyclic Codes

Let A=M2(ýý2+uýý2)$A=M_{2}(\mathbb {F}_{2}+u\mathbb {F}_{2})$, where u2 =ý0, the ring of 2 2 matrices over the finite ring ýý2+uýý2$\mathbb {F}_{2}+u\mathbb {F}_{2}$. The ring A is a non-commutative Frobenius ring but not a chain ring. In this paper, we ...

Let $p$ be an odd prime. Recently, Camarero and Martínez (in “Quasi-perfect Lee codes of radius 2 and arbitrarily large dimension”, IEEE Trans. Inform. Theory, vol. 62, no. 3, 2016) constructed some $p$ -ary 2-quasi-perfect Lee codes for $p\equiv \pm 5 \pmod {12}$ . In this paper, some ...

This paper describes how 2-adic numbers can be used to analyze the structure of binary cyclic codes and of cyclic codes defined over Z _2(a), aý2, the ring of integers modulo 2 ^a. It provides a 2-adic proof of a theorem of McEliece that characterizes the ...