Sep 18, 2017 · Abstract:Finite Frobenius rings have been characterized as precisely those finite rings satisfying the MacWilliams extension property, ...

Oct 22, 2024 · In conclusion, an Artinian ring has the MacWilliams property if and only if it is finitarily Frobenius, i.e., it is quasi-Frobenius and its ...

Nov 16, 2018 · In the present note we offer a generalization of Wood's characterization of finite. Frobenius rings as rings satisfying the MacWilliams ...

It is proved that a left Artinian ring has the left MacWilliams property if and only if it is left pseudo-injective and its finitary left socle embeds into ...

Abstract. Finite Frobenius rings have been characterized as precisely those finite rings satisfying the MacWilliams extension property, by work of Wood.

TL;DR: In this article , a complete answer to the problem of characterizing left Artinian rings which satisfy the (left or right) MacWilliams extension theorem ...

Bibliographic details on MacWilliams' extension theorem for infinite rings.

Sep 1, 2022 · MacWilliams proved that every finite field has the extension property for Hamming weight which was later extended in a seminal work by Wood ...

In 1962, MacWilliams proved that any Hamming weight isometry between two codes over a finite field extends to a monomial transformation of the ambient space [13] ...

Nov 23, 2022 · We also derive MacWilliams-type relations for complete and symmetrized weight enumerators. As an application, we construct several optimal ...