We suggest a Jacobi form over a number field Q(√5,i); for obtaining this, we use a linear code C over R:=F4+uF4, where u2=0. We introduce MacWilliams identities for both complete weight enumerator and symmetrized weight enumerator in higher genus g≥1 of a linear code over R. Finally, we give invariants via a self-dual code of even length over R.
Citation: Boran Kim, Chang Heon Kim, Soonhak Kwon, Yeong-Wook Kwon. Jacobi forms over number fields from linear codes[J]. AIMS Mathematics, 2022, 7(5): 8235-8249. doi: 10.3934/math.2022459
| [1] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2024, 11(3): 380-380. doi: 10.3934/environsci.2024018 |
| [2] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2025, 12(2): 252-252. doi: 10.3934/environsci.2025011 |
| [3] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2021, 8(2): 100-100. doi: 10.3934/environsci.2021007 |
| [4] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2023, 10(2): 245-245. doi: 10.3934/environsci.2023014 |
| [5] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2018, 5(1): 64-66. doi: 10.3934/environsci.2018.1.64 |
| [6] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2016, 3(1): 140-140. doi: 10.3934/environsci.2016.1.140 |
| [7] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2019, 6(4): 262-264. doi: 10.3934/environsci.2019.4.262 |
| [8] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2020, 7(2): 153-155. doi: 10.3934/environsci.2020009 |
| [9] | Yifeng Wang . Journal summary from Editor in Chief. AIMS Environmental Science, 2017, 4(2): 287-288. doi: 10.3934/environsci.2017.2.287 |
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We suggest a Jacobi form over a number field Q(√5,i); for obtaining this, we use a linear code C over R:=F4+uF4, where u2=0. We introduce MacWilliams identities for both complete weight enumerator and symmetrized weight enumerator in higher genus g≥1 of a linear code over R. Finally, we give invariants via a self-dual code of even length over R.
Dear Editorial Board Members and Readers:
It is my pleasure to share with you the year-end report for AIMS Environmental Science for 2021. The journal continues to improve its quality as indicated by steady increases in the number of manuscripts received and the number of articles published over the past three years. We have received 202 submissions with 40 published online. The top read article received more than 15980 downloads.
I would like to thank all the board members for serving on the Editorial Board and their dedication and contribution to the journal. The goal for 2022 is to solicit more papers and increase paper citations. We will try our best to reduce the processing time and supply with a better experience for publication. To recognize the contribution of the Editorial Board members and authors during the years, we will offer that (1) for authors invited the article processing charge (APC) is automatically waived and (2) each editorial board member is entitled for some waivers. I am looking forward to continuing working with you to make the AIMS Environmental Science a sustainable and impactful journal. Please don't hesitate to send me e-mails if you have new ideas and suggestions to help us to achieve this goal.
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Yifeng Wang, Ph.D.
Editor in Chief, AIMS Environmental Science
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Boran Kim, Chang Heon Kim, Soonhak Kwon, Yeong-Wook Kwon. Jacobi forms over number fields from linear codes[J]. AIMS Mathematics, 2022, 7(5): 8235-8249. doi: 10.3934/math.2022459
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