LRC codes over characteristic $2$
This work addresses the problem of constructing LRC codes for even characteristic, which is incremental as it builds upon prior methods.
The authors completed the construction of LRC codes for even characteristic, presenting a general method that yields linear LRC codes with length approximately q^4, dimension and distance on the order of q^4, and locality r = q-1, and specifically analyzed cases for q = 4 and q = 8.
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.