Abstract
It is shown that Tamo-Barg locally recoverable codes (LRCs) can be considered as subcodes of generalized Reed-Solomon (GRS) codes. Their encoding can be interpreted as sequential encoding with two particular constituent codes that depend on each other. The message constraint approach for finding subfield subcodes of GRS codes is transferred to this setting in order to obtain subfield subcodes of LRCs. The subcodes have the same locality as their parent codes, and at least their minimum distance.
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