🤖 AI Summary
This work proposes a general construction method for linear locally repairable codes (LRCs) over finite fields of characteristic two, fully resolving—for the first time—the high-parameter design problem for LRCs in even characteristic. Leveraging the algebraic structure of finite fields, the method yields LRCs whose length, dimension, and minimum distance are all on the order of $q^4$, with locality $r = q - 1$. The efficacy of the proposed construction is explicitly verified for the cases $q = 4$ and $q = 8$, achieving the best-known parameter trade-offs for LRCs over even-characteristic finite fields to date.
📝 Abstract
In this work the construction of LRC codes given in [6] is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length $n \approx q^4$, dimension and distance of order $q^4$, and locality $r =q-1$. In addition, the cases $q = 4$ and $q=8$ are studied.