Parity check systems of nonlinear codes over finite commutative Frobenius rings

Thomas Westerbäck

doi:10.3934/amc.2017035

Article Contents

2017, Volume 11, Issue 3: 409-427. Doi: 10.3934/amc.2017035

This issue Previous Article Next Article Complete characterization of the first descent point distribution for the k-error linear complexity of 2ⁿ-periodic binary sequences

Parity check systems of nonlinear codes over finite commutative Frobenius rings

Thomas Westerbäck

Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland

Received: March 2012

Revised: February 2016

Published: September 2017

The author acknowledges support from the Knut and Alice Wallenberg Foundation under grant KAW 2005.0098. This support was given during the beginning of the work on this paper while the author was affiliated at the Department of Mathematics, KTH, S-10044 Stockholm, Sweden.

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Abstract

The concept of parity check matrices of linear binary codes has been extended by Heden [10] to parity check systems of nonlinear binary codes. In the present paper we extend this concept to parity check systems of nonlinear codes over finite commutative Frobenius rings. Using parity check systems, results on how to get some fundamental properties of the codes are given. Moreover, parity check systems and its connection to characters is investigated and a MacWilliams type theorem on the distance distribution is given.

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Mathematics Subject Classification: Primary: 94B25, 94B60; Secondary: 13M99.

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References

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