From skew-cyclic codes to asymmetric quantum codes
We introduce an additive but not F4-linear map S from Fn4 To F24n and exhibit some of its interesting structural properties. If C is a linear [n, k, d]4-code, then S(C) is an additive (2n, 22k, 2d)4-code. If C is an additive cyclic code then S(C) is an additive quasi-cyclic code of index 2. Moreover...
Saved in:
Main Authors: | , , , |
---|---|
Other Authors: | |
Format: | Article |
Language: | English |
Published: |
2012
|
Subjects: | |
Online Access: | https://hdl.handle.net/10356/94141 http://hdl.handle.net/10220/7623 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Nanyang Technological University |
Language: | English |
id |
sg-ntu-dr.10356-94141 |
---|---|
record_format |
dspace |
spelling |
sg-ntu-dr.10356-941412023-02-28T19:24:27Z From skew-cyclic codes to asymmetric quantum codes Ezerman, Martianus Frederic Ling, San Sole, Patrick Yemen, Olfa School of Physical and Mathematical Sciences DRNTU::Science::Mathematics We introduce an additive but not F4-linear map S from Fn4 To F24n and exhibit some of its interesting structural properties. If C is a linear [n, k, d]4-code, then S(C) is an additive (2n, 22k, 2d)4-code. If C is an additive cyclic code then S(C) is an additive quasi-cyclic code of index 2. Moreover, if C is a module θ-cyclic code, a recently introduced type of code which will be explained below, then S(C) is equivalent to an additive cyclic code if n is odd and to an additive quasi-cyclic code of index 2 if n is even. Given any (n, M, d)4-code C, the code S(C) is self-orthogonal under the trace Hermitian inner product. Since the mapping S preserves nestedness, it can be used as a tool in constructing additive asymmetric quantum codes. Published version 2012-03-08T08:44:38Z 2019-12-06T18:51:25Z 2012-03-08T08:44:38Z 2019-12-06T18:51:25Z 2011 2011 Journal Article Ezerman, M. F., Ling, S., Solé, P., & Yemen, O. (2011). From skew-cyclic codes to asymmetric quantum codes. Advances in Mathematics of Communications, 5 (1), 41–57. https://hdl.handle.net/10356/94141 http://hdl.handle.net/10220/7623 10.3934/amc.2011.5.41 en Advances in mathematics of communications ©2011 The American Institute of Mathematical Sciences (AIMS) This paper was published in Advances in Mathematics of Communications and is made available as an electronic reprint (preprint) with permission of The American Institute of Mathematical Sciences AIMS.The paper can be found at http://dx.doi.org/10.3934/amc.2011.5.41. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 17 p. application/pdf |
institution |
Nanyang Technological University |
building |
NTU Library |
continent |
Asia |
country |
Singapore Singapore |
content_provider |
NTU Library |
collection |
DR-NTU |
language |
English |
topic |
DRNTU::Science::Mathematics |
spellingShingle |
DRNTU::Science::Mathematics Ezerman, Martianus Frederic Ling, San Sole, Patrick Yemen, Olfa From skew-cyclic codes to asymmetric quantum codes |
description |
We introduce an additive but not F4-linear map S from Fn4 To F24n and exhibit some of its interesting structural properties. If C is a linear [n, k, d]4-code, then S(C) is an additive (2n, 22k, 2d)4-code. If C is an additive cyclic code then S(C) is an additive quasi-cyclic code of index 2. Moreover, if C is a module θ-cyclic code, a recently introduced type of code which will be explained below, then S(C) is equivalent to an additive cyclic code if n is odd and to an additive quasi-cyclic code of index 2 if n is even. Given any (n, M, d)4-code C, the code S(C) is self-orthogonal under the trace Hermitian
inner product. Since the mapping S preserves nestedness, it can be used as a tool in constructing additive asymmetric quantum codes. |
author2 |
School of Physical and Mathematical Sciences |
author_facet |
School of Physical and Mathematical Sciences Ezerman, Martianus Frederic Ling, San Sole, Patrick Yemen, Olfa |
format |
Article |
author |
Ezerman, Martianus Frederic Ling, San Sole, Patrick Yemen, Olfa |
author_sort |
Ezerman, Martianus Frederic |
title |
From skew-cyclic codes to asymmetric quantum codes |
title_short |
From skew-cyclic codes to asymmetric quantum codes |
title_full |
From skew-cyclic codes to asymmetric quantum codes |
title_fullStr |
From skew-cyclic codes to asymmetric quantum codes |
title_full_unstemmed |
From skew-cyclic codes to asymmetric quantum codes |
title_sort |
from skew-cyclic codes to asymmetric quantum codes |
publishDate |
2012 |
url |
https://hdl.handle.net/10356/94141 http://hdl.handle.net/10220/7623 |
_version_ |
1759853801368453120 |