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Volume 31, Issue 4
Self-Dual Codes with Symplectic Inner Product

Jizhu Nan & Xuemin Yu

Commun. Math. Res., 31 (2015), pp. 345-350.

Published online: 2021-05

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  • Abstract

In this paper, we discuss a kind of Hermitian inner product — symplectic inner product, which is different from the original inner product — Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code $C$ over $F_p$ with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over $F_p$, which is simpler than others.

  • Keywords

symplectic inner product, symplectic self-dual code, symplectic circulant code.

  • AMS Subject Headings

94B05, 51A50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-345, author = {Jizhu and Nan and and 19314 and and Jizhu Nan and Xuemin and Yu and and 18748 and and Xuemin Yu}, title = {Self-Dual Codes with Symplectic Inner Product}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {345--350}, abstract = {

In this paper, we discuss a kind of Hermitian inner product — symplectic inner product, which is different from the original inner product — Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code $C$ over $F_p$ with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over $F_p$, which is simpler than others.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.06}, url = {http://global-sci.org/intro/article_detail/cmr/18916.html} }
TY - JOUR T1 - Self-Dual Codes with Symplectic Inner Product AU - Nan , Jizhu AU - Yu , Xuemin JO - Communications in Mathematical Research VL - 4 SP - 345 EP - 350 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.06 UR - https://global-sci.org/intro/article_detail/cmr/18916.html KW - symplectic inner product, symplectic self-dual code, symplectic circulant code. AB -

In this paper, we discuss a kind of Hermitian inner product — symplectic inner product, which is different from the original inner product — Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code $C$ over $F_p$ with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over $F_p$, which is simpler than others.

Jizhu Nan & Xuemin Yu. (2021). Self-Dual Codes with Symplectic Inner Product. Communications in Mathematical Research . 31 (4). 345-350. doi:10.13447/j.1674-5647.2015.04.06
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