@article{BULUT YILGÖR2025, 
author = {Merve BULUT YILGÖR},
title = {Cyclic codes over        F    2    [  u  ,  v  ,  w  ]      /    ⟨      u    2    =      v    2    ,  u  v  =  0  ,      w    2    =  w  ⟩ and its applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {28396-28406},
keywords = {algebraic coding theory, codes over rings, homogeneous weight},
url = {https://www.sciopen.com/article/10.3934/math.20251249},
doi = {10.3934/math.20251249},
abstract = {We investigate linear and cyclic codes over the ring        F    2    [  u  ,  v  ,  w  ]      /    ⟨      u    2    =      v    2    ,    u  v  =  0  ,        w    2    =  w  ⟩. This is a commutative Frobenius non-chain ring, which, to the best of our knowledge, is studied here for the first time in the literature. We define a homogeneous weight on the ring and, with respect to a Gray map induced by this weight, obtain the optimal Reed-Muller code    R  M    (  1  ,  7  ). We analyze the algebraic structure of the ring in detail, determine its ideals, and present code constructions together with their Gray images.}
}