多元微积分
二进制数
数学
二进制代码
离散数学
线性码
区块代码
组合数学
应用数学
算法
解码方法
算术
控制工程
工程类
作者
Jong Yoon Hyun,Jihye Jeong,Yoonjin Lee
标识
DOI:10.1109/tit.2024.3406798
摘要
We study the binary linear code families associated with certain types of multivariable functions. We observe that a majority of these codes are not optimal codes nor few weight codes yet. In this paper, we find infinite families of few weight (near-) optimal binary linear codes from our code families. Furthermore, we produce support t -designs ( t = 2 or 3) which cannot be determined by the Assmus-Mattson Theorem ; this is the first time that the result by Tang et al. was successfully used to prove that linear codes hold t -designs. As another application, we find many (near-) optimal quantum codes from the dual codes of our code families using the CSS construction . As a main method, we use the modified shortening method (simply, called shortening method ), which is applied to our code families. Using the results on the weight distributions of our shortened codes, we verify that our codes families support t -designs ( t = 2, 3).We emphasize that some infinite families of few weight optimal binary linear codes have new parameters.
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