Projective binary linear codes from special Boolean functions
Projective binary linear codes from special Boolean functions
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DOI：
10.1007/s00200-019-00412-z
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
Ziling Heng;Weiqiong Wang;Yan Wang
中科院分区：
文献类型：
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作者：
Ziling Heng;Weiqiong Wang;Yan Wang
具有少量权重的线性码在通信、秘密共享方案、认证码、关联方案、块设计等方面有很好的应用。投影二进制线性码是实际应用中最重要的线性码子类之一。本文的目的是用一些特殊的布尔函数构造投影二进制线性码。推导了具有三或四个权重的四族二进制线性码，并确定了它们的对偶参数。事实证明，这些代码的对偶相对于球堆积界限是最优或几乎最优的。作为应用，本文提出的代码可用于构造具有有趣的访问结构的关联方案和秘密共享方案。
Linear codes with a few weights have nice applications in communication, secret sharing schemes, authentication codes, association schemes, block designs and so on. Projective binary linear codes are one of the most important subclasses of linear codes for practical applications. The objective of this paper is to construct projective binary linear codes with some special Boolean functions. Four families of binary linear codes with three or four weights are derived and the parameters of their duals are also determined. It turns out that the duals of these codes are optimal or almost optimal with respect to the sphere-packing bound. As applications, the codes presented in this paper can be used to construct association schemes and secret sharing schemes with interesting access structures.