Character sums and MacWilliams identities

نویسندگان

  • Dae San Kim
  • Dong Chan Kim
چکیده

We show that certain character sums are intimately connected with MacWilliams identities for linear poset codes as well as usual linear codes. We also illustrate in some two poset codes that this method gives much shorter proofs than the ones using discrete Poisson summation formula. © 2004 Elsevier B.V. All rights reserved. MSC: primary 11L03; 94B60; secondary 94B05

برای دانلود 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

Fourier-reflexive partitions and MacWilliams identities for additive codes

A partition of a finite abelian group gives rise to a dual partition on the character group via the Fourier transform. Properties of the dual partitions are investigated and a convenient test is given for the case that the bidual partition coincides the primal partition. Such partitions permit MacWilliams identities for the partition enumerators of additive codes. It is shown that dualization c...

متن کامل

MacWilliams type identities on the Lee and Euclidean weights for linear codes over ℤℓ

Abstract Motivated by the works of Shiromoto [3] and Shi et al. [4], we study the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over Zl. Necessary and sufficient conditions for the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over Zl are given. Some examples about s...

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 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

Finite Trigonometric Character Sums via Discrete Fourier Analysis

We prove several old and new theorems about finite sums involving characters and trigonometric functions. These sums can be traced back to theta function identities from Ramanujan’s notebooks and were systematically first studied by Berndt and Zaharescu; their proofs involved complex contour integration. We show how to prove most of Berndt–Zaharescu’s and some new identities by elementary metho...

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

برای دانلود 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

عنوان ژورنال:
  • Discrete Mathematics

دوره 287  شماره 

صفحات  -

تاریخ انتشار 2004