New constructions of abelian non-cyclic orbit codes based on parabolic subgroups and tensor products
Orbit codes, as special constant dimension subspace codes, have attracted much attention due to their applications for error correction in random network coding. They arise as orbits of a subspace of Fqn under the action of some subgroup of the finite general linear group GLn(q). The main contributi...
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| Vydáno v: | Finite fields and their applications Ročník 103; s. 102587 |
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| Abstract | Orbit codes, as special constant dimension subspace codes, have attracted much attention due to their applications for error correction in random network coding. They arise as orbits of a subspace of Fqn under the action of some subgroup of the finite general linear group GLn(q). The main contribution of this paper is to propose new methods for constructing large non-cyclic orbit codes. First, using the subgroup structure of maximal subgroups of GLn(q), we propose a new construction of an abelian non-cyclic orbit codes of size qk with k≤n/2. The proposed code is shown to be a partial spread which in many cases is close to the known maximum-size codes. Next, considering a larger framework, we introduce the notion of tensor product operation for subspace codes and explicitly determine the parameters of such product codes. The parameters of the constructions presented in this paper improve the constructions already obtained in [6] and [7]. |
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| AbstractList | Orbit codes, as special constant dimension subspace codes, have attracted much attention due to their applications for error correction in random network coding. They arise as orbits of a subspace of Fqn under the action of some subgroup of the finite general linear group GLn(q). The main contribution of this paper is to propose new methods for constructing large non-cyclic orbit codes. First, using the subgroup structure of maximal subgroups of GLn(q), we propose a new construction of an abelian non-cyclic orbit codes of size qk with k≤n/2. The proposed code is shown to be a partial spread which in many cases is close to the known maximum-size codes. Next, considering a larger framework, we introduce the notion of tensor product operation for subspace codes and explicitly determine the parameters of such product codes. The parameters of the constructions presented in this paper improve the constructions already obtained in [6] and [7]. |
| ArticleNumber | 102587 |
| Author | Biranvand, Nader Askary, Soleyman Shirjian, Farrokh |
| Author_xml | – sequence: 1 givenname: Soleyman surname: Askary fullname: Askary, Soleyman email: s.asgary95@gmail.com – sequence: 2 givenname: Nader surname: Biranvand fullname: Biranvand, Nader email: nabiranvand@gmail.com – sequence: 3 givenname: Farrokh orcidid: 0000-0002-0459-3160 surname: Shirjian fullname: Shirjian, Farrokh email: fashirjian@gmail.com |
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| Cites_doi | 10.1007/s40314-023-02353-3 10.1007/s10623-012-9691-5 10.1016/j.disc.2020.112273 10.1016/j.ffa.2013.11.007 10.1109/TIT.2008.926449 10.1007/s12095-018-0306-5 10.1007/s10255-020-0974-8 10.1007/s10623-020-00823-x 10.3934/amc.2015.9.177 10.1109/18.850663 10.1080/00927872.2010.515521 10.3934/amc.2020035 10.1016/j.ffa.2022.102153 10.3934/amc.2021007 |
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| Title | New constructions of abelian non-cyclic orbit codes based on parabolic subgroups and tensor products |
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