Abstract
There is a local ring I of order 4, without identity for the multiplication, defined by generators and relations as
We study a recursive construction of self-orthogonal codes over I. We classify self orthogonal codes of length n and size \(2^n\) (called here quasi self-dual codes or QSD) up to the length \(n=6.\) In particular, we classify Type IV codes (QSD codes with even weights) and quasi Type IV codes (QSD codes with even torsion code) up to \(n=6.\)
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Acknowledgements
This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant Number KEP-PhD-29-130-40 . The authors, therefore, acknowledge with thanks DSR for technical and financial support.
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Communicated by J.-L. Kim.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”.
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Alahmadi, A., Alkathiry, A., Altassan, A. et al. The build-up construction over a commutative non-unital ring. Des. Codes Cryptogr. 90, 3003–3010 (2022). https://doi.org/10.1007/s10623-022-01044-0
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DOI: https://doi.org/10.1007/s10623-022-01044-0