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This content will become publicly available on March 25, 2026

Title: Good polynomials for locally recoverable codes: Classification results, asymptotics, and exact formulae
Let [Formula: see text] be a prime power and [Formula: see text]. In this paper we complete the classification of good polynomials of degree [Formula: see text] that achieve the best possible asymptotics (with an explicit error term) for the number of totally split places. Moreover, for degrees up to [Formula: see text], we provide an explicit lower bound and an asymptotic estimate for the number of totally split places of [Formula: see text]. Finally, we prove the general fact that the number [Formula: see text] of [Formula: see text] for which [Formula: see text] splits obeys a linear recurring sequence. For any [Formula: see text], this allows for the computation of [Formula: see text] for large [Formula: see text] by only computing a recurrence sequence over [Formula: see text].  more » « less
Award ID(s):
2338424
PAR ID:
10596753
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
World Scientific
Date Published:
Journal Name:
Journal of Algebra and Its Applications
ISSN:
0219-4988
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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