minimum distance code

简明释义

最小距离码

英英释义

例句

1.When designing a data transmission protocol, engineers often consider the properties of minimum distance codes 最小距离码 to ensure reliability.

在设计数据传输协议时，工程师通常会考虑最小距离码 minimum distance codes 的特性以确保可靠性。

2.The concept of minimum distance codes 最小距离码 is essential in the field of coding theory.

在编码理论领域，最小距离码 minimum distance codes 的概念至关重要。

3.The performance of a communication system can be greatly improved by using a minimum distance code 最小距离码 that minimizes the chance of overlap between codewords.

通过使用一个能够最小化码字重叠的最小距离码 minimum distance code，可以大大提高通信系统的性能。

4.A well-known example of a minimum distance code 最小距离码 is the Hamming code, which is used for single-error correction.

一个著名的最小距离码 minimum distance code 的例子是汉明码，它用于单错误纠正。

5.In error correction, a minimum distance code 最小距离码 is crucial for detecting and correcting multiple errors.

在错误纠正中，最小距离码 minimum distance code 对于检测和纠正多个错误至关重要。

作文

In the realm of coding theory, the concept of minimum distance code plays a crucial role in ensuring reliable data transmission. This term refers to the smallest Hamming distance between any two codewords in a given code. The significance of this distance lies in its ability to determine the error-correcting capability of the code. A larger minimum distance code implies that the code can correct more errors, making it essential for applications where data integrity is paramount, such as in telecommunications and data storage.To understand the importance of minimum distance code, we must first delve into the basics of coding theory. Codes are essentially sets of symbols or sequences used to represent information. In digital communications, these codes help in encoding data before transmission and decoding it upon reception. However, during transmission, data may become corrupted due to noise or interference. This is where the minimum distance code comes into play.For instance, consider a simple binary code where the codewords are represented as sequences of zeros and ones. If we have two codewords, '000' and '111', the Hamming distance between them is three, which means they differ in all three positions. In this case, the minimum distance code is three. This distance indicates that if up to one error occurs during transmission, the receiver can still accurately decode the intended message by recognizing the closest valid codeword.The relationship between minimum distance code and error correction is further exemplified by the well-known Hamming code. Hamming codes are designed with a minimum distance code of three, allowing them to detect up to two errors and correct one error in the transmitted data. This capability is vital for maintaining the accuracy of information, especially in critical systems like satellite communications or financial transactions.Moreover, the design of codes with optimal minimum distance code is an ongoing area of research. Engineers and computer scientists continually seek to create codes that maximize error correction while minimizing redundancy. This balance is crucial because excessive redundancy can lead to inefficient use of bandwidth and storage space. Therefore, understanding and applying the principles of minimum distance code is essential for developing efficient coding schemes.In conclusion, the concept of minimum distance code is fundamental to coding theory and has far-reaching implications in the field of data communication. By ensuring that codes possess an adequate minimum distance code, engineers can enhance the reliability of data transmission, thereby safeguarding the integrity of information in our increasingly digital world. As technology continues to evolve, the study and application of minimum distance code will remain a critical focus for researchers and practitioners alike, ensuring that our communication systems remain robust against errors and disturbances.

在编码理论领域，最小距离码的概念在确保可靠数据传输方面发挥着至关重要的作用。这个术语指的是给定代码中任何两个码字之间的最小汉明距离。这个距离的重要性在于它能够决定代码的纠错能力。更大的最小距离码意味着该代码可以纠正更多的错误，这对于数据完整性至关重要的应用程序（如电信和数据存储）来说是必不可少的。要理解最小距离码的重要性，我们首先需要深入了解编码理论的基础。代码本质上是一组用于表示信息的符号或序列。在数字通信中，这些代码帮助在传输之前对数据进行编码，并在接收时对其进行解码。然而，在传输过程中，由于噪声或干扰，数据可能会受到损坏。这就是最小距离码发挥作用的地方。例如，考虑一个简单的二进制代码，其中码字表示为零和一的序列。如果我们有两个码字，'000'和'111'，它们之间的汉明距离为三，这意味着它们在所有三个位置上都不同。在这种情况下，最小距离码为三。这个距离表明，如果在传输过程中发生最多一个错误，接收方仍然可以通过识别最接近的有效码字来准确解码预期消息。最小距离码与错误纠正之间的关系在著名的汉明码中得到了进一步的体现。汉明码的设计具有最小距离码为三的特点，使其能够检测最多两个错误并纠正一个错误。这种能力对于维护信息的准确性至关重要，尤其是在卫星通信或金融交易等关键系统中。此外，具有最佳最小距离码的代码设计仍然是一个持续研究的领域。工程师和计算机科学家不断寻求创建最大化纠错能力同时最小化冗余的代码。这种平衡至关重要，因为过多的冗余可能导致带宽和存储空间的低效使用。因此，理解和应用最小距离码的原理对于开发高效的编码方案至关重要。总之，最小距离码的概念是编码理论的基础，对数据通信领域具有深远的影响。通过确保代码具备足够的最小距离码，工程师可以增强数据传输的可靠性，从而保护我们日益数字化世界中信息的完整性。随着技术的不断发展，最小距离码的研究和应用将继续成为研究人员和从业者的重点，确保我们的通信系统在面对错误和干扰时保持稳健。