A further study on the mass formula for linear codes with prescribed hull dimension
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929547970084864 |
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| author | Li, Shitao Shi, Minjia Li, Yang Ling, San |
| author_facet | Li, Shitao Shi, Minjia Li, Yang Ling, San |
| contents | Finding a mass formula for a given class of linear codes is a fundamental problem in combinatorics and coding theory. In this paper, we consider the action of the unitary (resp. symplectic) group on the set of all Hermitian (resp. symplectic) linear complementary dual (LCD) codes, prove that all Hermitian (resp. symplectic) LCD codes are on a unique orbit under this action, and determine the formula for the size of the orbit. Based on this, we develop a general technique to obtain a closed mass formula for linear codes with prescribed Hermitian (resp. symplectic) hull dimension, and further obtain some asymptotic results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A further study on the mass formula for linear codes with prescribed hull dimension Li, Shitao Shi, Minjia Li, Yang Ling, San Information Theory Combinatorics Finding a mass formula for a given class of linear codes is a fundamental problem in combinatorics and coding theory. In this paper, we consider the action of the unitary (resp. symplectic) group on the set of all Hermitian (resp. symplectic) linear complementary dual (LCD) codes, prove that all Hermitian (resp. symplectic) LCD codes are on a unique orbit under this action, and determine the formula for the size of the orbit. Based on this, we develop a general technique to obtain a closed mass formula for linear codes with prescribed Hermitian (resp. symplectic) hull dimension, and further obtain some asymptotic results. |
| title | A further study on the mass formula for linear codes with prescribed hull dimension |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2410.13578 |