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Influences of
some families of error-correcting codes
Hailey Egan, Jason T. LeGrow, Gretchen L. Matthews and Jeff Suliga |
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Vol. 18 (2025), No. 2, 329–349
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Abstract |
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The ability of a linear error-correcting code to recover erasures is connected to influences of particular monotone Boolean functions. These functions provide insight into the role that particular coordinates play in a code’s erasure repair capability. We consider directly the influences of coordinates of a code. We describe a family of codes, called codes with minimum disjoint support, for which all influences may be determined. As a consequence, we find influences of repetition codes and certain distinct weight codes. Computing influences is typically circumvented by appealing to the transitivity of the automorphism group of the code. Some of the codes considered here fail to meet the transitivity conditions required for these standard approaches, yet we can compute them directly. |
Keywords
boolean functions, error-correcting codes
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Mathematical Subject Classification
Primary: 94B05, 94B60
Secondary: 94D10
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Milestones
Received: 1 August 2023
Revised: 5 October 2023
Accepted: 18 October 2023
Published: 26 February 2025
Communicated by Joshua Cooper
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Authors |
| Hailey Egan | |
| Virginia Tech Blacksburg, VA United States |
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| Jason T. LeGrow | |
| Virginia Tech Blacksburg, VA United States |
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| Gretchen L. Matthews | |
| Virginia Tech Blacksburg, VA United States |
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| Jeff Suliga | |
| Virginia Tech Blacksburg, VA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
