A $q$-Polymatroid Framework for Information Leakage in Secure Linear Network Coding
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914248288894976 |
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| author | Byrne, Eimear Dinesen, Johan Vester Freij-Hollanti, Ragnar Hollanti, Camilla |
| author_facet | Byrne, Eimear Dinesen, Johan Vester Freij-Hollanti, Ragnar Hollanti, Camilla |
| contents | We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes a subset of network links is characterized by the conditional rank function of a representable $q$-polymatroid associated with the underlying rank-metric code pair. Building on this connection, we introduce the notions of $q$-polymatroid ports and $q$-access structures and describe their structural properties. Moreover, we extend Massey's correspondence between minimal codewords and minimal access sets to the rank-metric setting and prove a $q$-analogue of the Brickell--Davenport theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07567 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A $q$-Polymatroid Framework for Information Leakage in Secure Linear Network Coding Byrne, Eimear Dinesen, Johan Vester Freij-Hollanti, Ragnar Hollanti, Camilla Information Theory We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes a subset of network links is characterized by the conditional rank function of a representable $q$-polymatroid associated with the underlying rank-metric code pair. Building on this connection, we introduce the notions of $q$-polymatroid ports and $q$-access structures and describe their structural properties. Moreover, we extend Massey's correspondence between minimal codewords and minimal access sets to the rank-metric setting and prove a $q$-analogue of the Brickell--Davenport theorem. |
| title | A $q$-Polymatroid Framework for Information Leakage in Secure Linear Network Coding |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.07567 |