One‑Weight <italic style="font-style: italic">ZpZp</italic>[<italic style="font-style: italic">u</italic>]‑Additive Codes

WU Bo; SHI Min-jia; LI Tian-tian; TENG Ao

doi:10.12263/DZXB.20210108

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One‑Weight Z_pZ_p[u]‑Additive Codes

CORRESPONDENCE | 更新时间：2025-12-08

- One‑Weight Z_pZ_p[u]‑Additive Codes
- ACTA ELECTRONICA SINICA Vol. 49, Issue 9, Pages: 1857-1862(2021)
- 作者机构：
  
  1.中国科学院信息工程研究所信息安全国家重点实验室,北京 100093
  2.中国科学院大学网络空间安全学院,北京 101408
  3.安徽大学数学科学学院,安徽合肥 230601
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20210108
  CLC： TN911.22
- Received：13 January 2021，
  
  Revised：2021-02-27，
  
  Published：25 September 2021
- 稿件说明：
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吴波,施敏加,李甜甜等.1‑重量Z_pZ_p[u]‑加性码[J].电子学报,2021,49(09):1857-1862.

WU Bo,SHI Min-jia,LI Tian-tian,et al.One‑Weight Z_pZ_p[u]‑Additive Codes[J].ACTA ELECTRONICA SINICA,2021,49(09):1857-1862.
吴波,施敏加,李甜甜等.1‑重量Z_pZ_p[u]‑加性码[J].电子学报,2021,49(09):1857-1862. DOI： 10.12263/DZXB.20210108.

WU Bo,SHI Min-jia,LI Tian-tian,et al.One‑Weight Z_pZ_p[u]‑Additive Codes[J].ACTA ELECTRONICA SINICA,2021,49(09):1857-1862. DOI： 10.12263/DZXB.20210108.

摘要

本文定义了1‑重量

[

]‑加性码

其中

是奇素数. 给出并证明

[

]‑加性码及其对偶码之间的MacWilliams恒等式

并利用此恒等式得出1‑重量加性码的对偶码最小距离的一个下界. 给出1‑重量加性码的结构性质. 证明了在Gray映射下

1‑重量

[

]‑加性码的像是1‑Hamming重量

‑元最优线性码

达到Plotkin界和Griesmer界. 最后给出1‑重量

[

]‑加性码的一些构造.

Abstract

We devote to studying one‑weight

[

]‑additive codes

where

is an odd prime number. We derive a MacWilliams‑type identity that relates the weight enumerators of a

[

]‑additive code with its dual

and obtain a lower bound for the minimum distance of dual codes of one‑weight additive codes. Some structural properties of one‑weight

[

]‑additive codes are considered. By the Gray map

we obtain a family of optimal one‑Hamming weight

‑ary codes from one‑weight

[

]‑additive codes

which attain the Plotkin bound and Griesmer bound. Additionally

we describe some constructions of one‑weight

[

]‑additive codes.

关键词

Keywords

references

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⁰

One‑Weight ZpZp[u]‑Additive Codes

DOI：10.12263/DZXB.20210108

摘要

Abstract

关键词

Keywords

references

One‑Weight Z_pZ_p[u]‑Additive Codes