The equivalent identities of the MacWilliams identity for linear codes

نویسنده

  • Xiaomin Bao
چکیده

Abstract We use derivatives to prove the equivalences between MacWilliams identity and its four equivalent forms, and present new interpretations for the four equivalent forms. Our results explicitly give out the relationships between MacWilliams identity and its four equivalent forms.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

MacWilliams Identity for Codes with the Rank Metric

The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we derive the MacWilliams identity for linear codes with the rank metric, and our identity has a different form than that by Delsarte. Using our MacWilliams identity, we also derive related identities for...

متن کامل

Foundations of Linear Codes Defined over Finite Modules: the Extension Theorem and the Macwilliams Identities — Based on Lectures for the Cimpa-unesco-tübi̇tak Summer School

This paper discusses the foundations of the theory of linear codes defined over finite modules. Two topics are examined in depth: the extension theorem and the MacWilliams identities. Both of these topics were studied originally by MacWilliams in the context of linear codes defined over finite fields.

متن کامل

MacWilliams Type identities for $m$-spotty Rosenbloom-Tsfasman weight enumerators over finite commutative Frobenius rings

The m-spotty byte error control codes provide a good source for detecting and correcting errors in semiconductor memory systems using high density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). m-spotty byte error control codes are very suitable for burst correction. M. Özen and V. Siap [7] proved a MacWilliams identity for the m-spotty Rosenbloom-Tsfasman (shortly RT) weight enumerator...

متن کامل

Lecture Notes on Linear Codes Defined over Finite Modules: the Extension Theorem and the Macwilliams Identities — for Use of Cimpa-unesco-tübitak Summer

These lecture notes discuss the extension problem and the MacWilliams identities for linear codes defined over finite modules.

متن کامل

MacWilliams Identity for Codes with the Hamming and Rank Metrics

The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we first provide an alternative proof to the MacWilliams identity for linear codes with the Hamming metric. An intermediate result of our approach is that the Hamming weight enumerator of the dual of any ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1401.3582  شماره 

صفحات  -

تاریخ انتشار 2013