On skew polynomial codes and lattices from quotients of cyclic division algebras

Abstract

We propose a variation of Construction A of lattices from linear codes defined using the quotient Λ/pΛ of some order Λ inside a cyclic division F -algebra, for p a prime ideal of a number field F . To obtain codes over this quotient, we first give an isomorphism between Λ/pΛ and a ring of skew polynomials. We then discuss definitions and basic properties of… (More)

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