Optimal quinary cyclic codes with minimum distance four
Cyclic codes are an extremely important subclass of linear codes.They are widely used in the communication systems and data storage systems because they have efficient encoding and decoding algorithm.Until now,how to construct the optimal ternary cyclic codes has received a lot of attention and much...
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Editorial Department of Journal on Communications
2017-02-01
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| Series: | Tongxin xuebao |
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| Online Access: | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2017030/ |
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| author | Ye TIAN Yu-qing ZHANG Yu-pu HU |
| author_facet | Ye TIAN Yu-qing ZHANG Yu-pu HU |
| author_sort | Ye TIAN |
| collection | DOAJ |
| description | Cyclic codes are an extremely important subclass of linear codes.They are widely used in the communication systems and data storage systems because they have efficient encoding and decoding algorithm.Until now,how to construct the optimal ternary cyclic codes has received a lot of attention and much progress has been made.However,there is less research about the optimal quinary cyclic codes.Firstly,an efficient method to determine if cyclic codes C<sub>(1,e,t)</sub>were optimal codes was obtained.Secondly,based on the proposed method,when the equation e=5<sub>k</sub>+1 or e=5<sub>m</sub>−2hold,the theorem that the cyclic codes C<sub>(1,e,t)</sub>were optimal quinary cyclic codes was proved.In addition,perfect nonlinear monomials were used to construct optimal quinary cyclic codes with parameters[5<sub>m</sub>−1,5<sub>m</sub>−2m−2,4]optimal quinary cyclic codes over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>5</mn> <mi>m</mi> </msup> </mrow> </msub> </math></inline-formula>. |
| format | Article |
| id | doaj-art-4653f0c2be574b6d8a332e8bc633fd8a |
| institution | Kabale University |
| issn | 1000-436X |
| language | zho |
| publishDate | 2017-02-01 |
| publisher | Editorial Department of Journal on Communications |
| record_format | Article |
| series | Tongxin xuebao |
| spelling | doaj-art-4653f0c2be574b6d8a332e8bc633fd8a2025-01-14T07:11:39ZzhoEditorial Department of Journal on CommunicationsTongxin xuebao1000-436X2017-02-0138748059707259Optimal quinary cyclic codes with minimum distance fourYe TIANYu-qing ZHANGYu-pu HUCyclic codes are an extremely important subclass of linear codes.They are widely used in the communication systems and data storage systems because they have efficient encoding and decoding algorithm.Until now,how to construct the optimal ternary cyclic codes has received a lot of attention and much progress has been made.However,there is less research about the optimal quinary cyclic codes.Firstly,an efficient method to determine if cyclic codes C<sub>(1,e,t)</sub>were optimal codes was obtained.Secondly,based on the proposed method,when the equation e=5<sub>k</sub>+1 or e=5<sub>m</sub>−2hold,the theorem that the cyclic codes C<sub>(1,e,t)</sub>were optimal quinary cyclic codes was proved.In addition,perfect nonlinear monomials were used to construct optimal quinary cyclic codes with parameters[5<sub>m</sub>−1,5<sub>m</sub>−2m−2,4]optimal quinary cyclic codes over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>5</mn> <mi>m</mi> </msup> </mrow> </msub> </math></inline-formula>.http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2017030/finite fieldcyclic codesminimum distanceperfect nonlinear function |
| spellingShingle | Ye TIAN Yu-qing ZHANG Yu-pu HU Optimal quinary cyclic codes with minimum distance four Tongxin xuebao finite field cyclic codes minimum distance perfect nonlinear function |
| title | Optimal quinary cyclic codes with minimum distance four |
| title_full | Optimal quinary cyclic codes with minimum distance four |
| title_fullStr | Optimal quinary cyclic codes with minimum distance four |
| title_full_unstemmed | Optimal quinary cyclic codes with minimum distance four |
| title_short | Optimal quinary cyclic codes with minimum distance four |
| title_sort | optimal quinary cyclic codes with minimum distance four |
| topic | finite field cyclic codes minimum distance perfect nonlinear function |
| url | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2017030/ |
| work_keys_str_mv | AT yetian optimalquinarycycliccodeswithminimumdistancefour AT yuqingzhang optimalquinarycycliccodeswithminimumdistancefour AT yupuhu optimalquinarycycliccodeswithminimumdistancefour |