کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4655378 1632947 2014 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
MacWilliams' Extension Theorem for bi-invariant weights over finite principal ideal rings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
MacWilliams' Extension Theorem for bi-invariant weights over finite principal ideal rings
چکیده انگلیسی

A finite ring R and a weight w on R satisfy the Extension Property if every R-linear w-isometry between two R  -linear codes in RnRn extends to a monomial transformation of RnRn that preserves w. MacWilliams proved that finite fields with the Hamming weight satisfy the Extension Property. It is known that finite Frobenius rings with either the Hamming weight or the homogeneous weight satisfy the Extension Property. Conversely, if a finite ring with the Hamming or homogeneous weight satisfies the Extension Property, then the ring is Frobenius.This paper addresses the question of a characterization of all bi-invariant weights on a finite ring that satisfy the Extension Property. Having solved this question in previous papers for all direct products of finite chain rings and for matrix rings, we have now arrived at a characterization of these weights for finite principal ideal rings, which form a large subclass of the finite Frobenius rings. We do not assume commutativity of the rings in question.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 125, July 2014, Pages 177–193
نویسندگان
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