Abstract
In previous study, few-weight optimal codes were constructed by working on defining sets on the rings \({\mathbb {F}}_q[u]/(u^2)\), \({\mathbb {F}}_q[u]/(u^2-u)\) and \({\mathbb {F}}_q[u,v]/(u^2,v^2)\). We give a unified approach of this construction on a general \({\mathbb {F}}_q\)-algebra R. By applying this approach to the special case \(R={\mathbb {F}}_q[u]/(u^r)\), we construct many new classes of linear codes, decide their weight enumerators and show that they are new two or three-weight codes optimal or distance optimal to the Griesmer bound.
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Wang, S., Ouyang, Y. & Xie, X. A unified construction of optimal and distance optimal two or three-weight codes. J. Appl. Math. Comput. 69, 2695–2715 (2023). https://doi.org/10.1007/s12190-023-01852-0
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DOI: https://doi.org/10.1007/s12190-023-01852-0