The study entitled “Linear Codes over F_qx(F_q+vF_q)” led by ITU  Department of Mathematics members Res. Asst. Mevlüt TEKKOYUN and Doç. Dr. Ergün YARANERİ were published in “Journal of Applied Mathematics and Computing”.

Let R be the F_q-algebra F_q × (F_q + v F_q) of order q³ where v² = v and F_q is a finite field of q elements. They study linear codes over R, not only generalizing most of the existing results for q = 2 but also adding some new results. Their work is quite comprehensive including standard forms of generator matrices, free codes, dual codes, cyclic codes.

https://link.springer.com/content/pdf/10.1007/s12190-023-01893-5.pdf