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首页> 外文期刊>Information Theory, IEEE Transactions on >${BBZ}_4$ -Valued Quadratic Forms and Quaternary Sequence Families
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${BBZ}_4$ -Valued Quadratic Forms and Quaternary Sequence Families

机译：$ {BBZ} _4 $-值二次型和四级序列族

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摘要

In this paper, ${BBZ}_4$-valued quadratic forms defined on a vector space over ${rm GF}(2)$ are studied. A classification of such forms is established, distinguishing ${BBZ}_4$ -valued quadratic forms only by their rank and whether the associated bilinear form is alternating. This result is used to compute the distribution of certain exponential sums, which occur frequently in the analysis of quaternary codes and quaternary sequence sets. The concept is applied as follows. When $t=0$ or $m$ is odd, the correlation distribution of family $S(t)$, consisting of quaternary sequences of length $2^m-1$, is established. Then, motivated by practical considerations, a subset $S^*(t)$ of family $S(t)$ is defined, and the correlation distribution of family $S^*(t)$ is given for odd and even $m$.
机译：在本文中，研究了在$ {rm GF}（2）$上的向量空间上定义的$ {BBZ} _4 $值二次形式。建立这样的形式的分类，仅通过它们的等级以及相关联的双线性形式是否交替来区分$ {BBZ} _4 $值的二次形式。此结果用于计算某些指数和的分布，这些分布在分析四进制码和四进制序列集时经常出现。该概念如下应用。当$ t = 0 $或$ m $为奇数时，建立了由长度为$ 2 ^ m-1 $的四元序列组成的族$ S（t）$的相关分布。然后，出于实际考虑，定义了家庭$ S（t）$的子集$ S ^ *（t）$，给出了奇数$ m和偶数$ m的家庭$ S ^ *（t）$的相关分布。 $。

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