Codes from Layers of Hamming Graphs Full article
| Conference |
XIX International Symposium on Problems of Redundancy in Information and Control Systems 05-07 Nov 2025 , Москва |
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| Source | XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy) Compilation, 2025. |
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| Output data | Year: 2025, Pages: 1-5 Pages count : 5 DOI: 10.1109/redundancy68069.2025.11301429 | ||||
| Tags | codes from graphs, matrix rank, minimum distance problem, biregular parity check matrix, locally recoverable codes | ||||
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
We study the class of codes defined by the row space of the minimum distance relation matrix of t th and l th layers of Hamming graph H(m,q). By concatenating such matrices we obtain many distance-optimal codes of length up to 128. For arbitrary q,t,n,k we prove an analogue of a well-known Wilson rank formula [12] and find the dimensions of the codes in this class. For t=l−1, the codes are locally recoverable and include the codes from work of [11] for q=2. We show that the codes with q=2 are optimal locally-recoverable codes in our class.
Cite:
Danilko V.
, Mogilnykh I.
Codes from Layers of Hamming Graphs
In compilation XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). 2025. – C.1-5. DOI: 10.1109/redundancy68069.2025.11301429 OpenAlex
Codes from Layers of Hamming Graphs
In compilation XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). 2025. – C.1-5. DOI: 10.1109/redundancy68069.2025.11301429 OpenAlex
Dates:
| Published online: | Dec 23, 2025 |
Identifiers:
| OpenAlex: | W7116886765 |
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