weight enumerator

简明释义

权重计数子

英英释义

例句

1.The weight enumerator is crucial for analyzing the performance of error-correcting codes.

对于分析纠错码的性能，权重枚举器至关重要。

2.In coding theory, the weight enumerator helps in determining the number of codewords at each weight.

在编码理论中，权重枚举器有助于确定每个权重的码字数量。

3.Researchers often use the weight enumerator to evaluate the effectiveness of different coding schemes.

研究人员常常使用权重枚举器来评估不同编码方案的有效性。

4.The polynomial generated by the weight enumerator provides insights into the structure of the code.

由权重枚举器生成的多项式提供了对代码结构的洞察。

5.To improve data transmission reliability, we calculated the weight enumerator for our new code.

为了提高数据传输的可靠性，我们计算了新编码的权重枚举器。

作文

In the field of coding theory, one of the essential tools used to analyze the performance and efficiency of codes is the concept of a weight enumerator. The weight enumerator is a polynomial that provides valuable information about the weight distribution of a linear code. Specifically, it counts the number of codewords for each possible weight, where the weight of a codeword is defined as the number of non-zero components in that codeword. This is crucial because the weight of codewords directly affects the error-correcting capabilities of the code. Understanding the weight enumerator can greatly enhance our comprehension of how codes function under various conditions. For instance, when transmitting data over a noisy channel, it is vital to know how many codewords exist for each weight. A higher number of low-weight codewords may lead to an increased likelihood of undetected errors. Conversely, if a code has a well-balanced weight enumerator, it suggests that the code can perform efficiently across different noise levels. The mathematical representation of a weight enumerator is typically expressed as a polynomial, where the coefficients indicate the number of codewords corresponding to each weight. For example, if we denote the weight enumerator of a code by W(x), it can be formulated as: W(x) = A_0 + A_1x + A_2x^2 + ... + A_nx^n, where A_i represents the number of codewords with weight i. Analyzing this polynomial allows researchers and engineers to derive various properties of the code, such as its minimum distance, which is critical for determining the code's error correction capability. Moreover, the weight enumerator plays a significant role in the design of new codes. By understanding the weight distribution of existing codes through their weight enumerator, developers can create new codes with improved performance characteristics. This is particularly important in applications like data storage and communication systems, where reliability and efficiency are paramount. In conclusion, the weight enumerator is a fundamental concept in coding theory that encapsulates the weight distribution of a linear code. Its importance cannot be overstated, as it provides insights into the error-correcting capabilities of codes and aids in the development of new coding schemes. As technology continues to evolve, the role of the weight enumerator will remain critical in ensuring efficient and reliable data transmission and storage solutions.

在编码理论领域，一个用于分析代码性能和效率的重要工具是权重枚举器的概念。权重枚举器是一个多项式，它提供了关于线性码权重分布的宝贵信息。具体而言，它计算每个可能权重的码字数量，其中码字的权重被定义为该码字中非零分量的数量。这一点至关重要，因为码字的权重直接影响到代码的纠错能力。理解权重枚举器可以大大增强我们对代码在各种条件下如何工作的理解。例如，在嘈杂信道上发送数据时，了解每个权重有多少个码字是至关重要的。较高的低权重码字数量可能导致未检测到错误的可能性增加。相反，如果一个代码具有良好平衡的权重枚举器，则表明该代码能够在不同噪声水平下高效运行。权重枚举器的数学表示通常以多项式形式表达，其中系数表示与每个权重对应的码字数量。例如，如果我们用W(x)表示一个代码的权重枚举器，它可以被公式化为：W(x) = A_0 + A_1x + A_2x^2 + ... + A_nx^n，其中A_i表示权重为i的码字数量。分析这个多项式使研究人员和工程师能够推导出代码的各种属性，例如其最小距离，这对于确定代码的错误更正能力至关重要。此外，权重枚举器在新代码设计中也发挥着重要作用。通过理解现有代码的权重分布（通过它们的权重枚举器），开发者可以创建具有更好性能特征的新代码。这在数据存储和通信系统等应用中尤为重要，因为可靠性和效率至关重要。总之，权重枚举器是编码理论中的一个基本概念，它概括了线性码的权重分布。它的重要性不容小觑，因为它提供了对代码纠错能力的洞察，并有助于新编码方案的发展。随着技术的不断发展，权重枚举器的角色将在确保高效和可靠的数据传输与存储解决方案中继续发挥关键作用。