在Matlab中获得所有可能的位翻转组合，用于CRC计算_Matlab_Combinations_Bit_Combinatorics_Crc

在Matlab中获得所有可能的位翻转组合，用于CRC计算

matlab

在Matlab中获得所有可能的位翻转组合，用于CRC计算,matlab,combinations,bit,combinatorics,crc,Matlab,Combinations,Bit,Combinatorics,Crc,我正在用Matlab做一些CRC测试。我有一个CRC-8函数，我想知道哪种位翻转组合会导致完全相同的CRC 让我们考虑一组类似的位。 Input = [1,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1]; 我现在如何处理所有可能的位翻转组合？我做了一些研究，但没有找到一个好的答案，也许你能帮上忙。CRC-8有八个位代表输入位字符串的签名：您的实验可以是生成所有可能的长度为n的2^n不同输入位字符串，并注册导致给定签名的所有字符串请注意，每次实验都必须从相同的初始8位状态字开

我正在用Matlab做一些CRC测试。我有一个CRC-8函数，我想知道哪种位翻转组合会导致完全相同的CRC

让我们考虑一组类似

的位。

Input = [1,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1];

我现在如何处理所有可能的位翻转组合？我做了一些研究，但没有找到一个好的答案，也许你能帮上忙。

CRC-8有八个位代表输入位字符串的签名：

您的实验可以是生成所有可能的长度为

的

2^n

不同输入位字符串，并注册导致给定签名的所有字符串

请注意，每次实验都必须从相同的初始8位状态字开始

您的示例输入为16位长。16位可能存在不同的位字符串。尝试每种方法，找出哪些字符串与输入的签名相同

要了解

CRC-8

电路的操作，请查看一个在线提供的动画

CRC计算器

。你也可以看看维基百科上的文章

使用

程序（见下文），我完成了这个实验。无论输入位字符串的顺序如何（从左到右，反之亦然），65536位字符串中的256位具有相同的签名。8位散列方法只提供256个不同的签名，我们还能从中期待什么呢

我的代码：

using System;

namespace akCrc8Eval
{
    class Crc8Evaluator
    {
        // CRC 8 lookup table
        // https://github.com/WasatchPhotonics/CRC8_Example
        private static byte[] CRC_8_TABLE =
            {
              0, 94,188,226, 97, 63,221,131,194,156,126, 32,163,253, 31, 65,
            157,195, 33,127,252,162, 64, 30, 95,  1,227,189, 62, 96,130,220,
             35,125,159,193, 66, 28,254,160,225,191, 93,  3,128,222, 60, 98,
            190,224,  2, 92,223,129, 99, 61,124, 34,192,158, 29, 67,161,255,
             70, 24,250,164, 39,121,155,197,132,218, 56,102,229,187, 89,  7,
            219,133,103, 57,186,228,  6, 88, 25, 71,165,251,120, 38,196,154,
            101, 59,217,135,  4, 90,184,230,167,249, 27, 69,198,152,122, 36,
            248,166, 68, 26,153,199, 37,123, 58,100,134,216, 91,  5,231,185,
            140,210, 48,110,237,179, 81, 15, 78, 16,242,172, 47,113,147,205,
             17, 79,173,243,112, 46,204,146,211,141,111, 49,178,236, 14, 80,
            175,241, 19, 77,206,144,114, 44,109, 51,209,143, 12, 82,176,238,
             50,108,142,208, 83, 13,239,177,240,174, 76, 18,145,207, 45,115,
            202,148,118, 40,171,245, 23, 73,  8, 86,180,234,105, 55,213,139,
             87,  9,235,181, 54,104,138,212,149,203, 41,119,244,170, 72, 22,
            233,183, 85, 11,136,214, 52,106, 43,117,151,201, 74, 20,246,168,
            116, 42,200,150, 21, 75,169,247,182,232, 10, 84,215,137,107, 53
        };

        // Calculate 8-bit signature for byte array
        // inspired by:  https://github.com/WasatchPhotonics/CRC8_Example
        public byte Calc_CRC_8(byte[] DataArray, int Length)
        {
            byte CRC = 0;  //  initial value always 0

            for (int i = 0; i < Length; i++)
            {
                CRC = CRC_8_TABLE[CRC ^ DataArray[i]];
            }

            return CRC;
        }

        // Calculate 8-bit signature for 16-bit unsigned int
        private byte Calc_CRC_8(UInt16 n)
        {
            const int DIM = 16;
            byte CRC = 0;  //  initial value always 0

            for (int i = 0; i < DIM; i++)
            {
                byte b = (byte)(((n & (1 << i)) == 0) ? 0 : 1);
                CRC = CRC_8_TABLE[CRC ^ b];
            }

            return CRC;
        }

        public void getBitStringsWithSameSignature(byte[] bytes)
        {
            byte sig = Calc_CRC_8(bytes, bytes.Length);
            int count = 0;

            for (int n = 0; n < UInt16.MaxValue; n++)
            {
                if (sig == Calc_CRC_8((UInt16)n))
                {
                    count++;
                }
            }

            Console.WriteLine($"Found {count} bit-strings with signature {sig}");
        }
    }
}

使用系统；
命名空间akCrc8Eval
{
类Crc8Evaluator
{
//CRC 8查找表
// https://github.com/WasatchPhotonics/CRC8_Example
专用静态字节[]CRC_8_表=
{
0, 94,188,226, 97, 63,221,131,194,156,126, 32,163,253, 31, 65,
157,195, 33,127,252,162, 64, 30, 95,  1,227,189, 62, 96,130,220,
35,125,159,193, 66, 28,254,160,225,191, 93,  3,128,222, 60, 98,
190,224,  2, 92,223,129, 99, 61,124, 34,192,158, 29, 67,161,255,
70, 24,250,164, 39,121,155,197,132,218, 56,102,229,187, 89,  7,
219,133,103, 57,186,228,  6, 88, 25, 71,165,251,120, 38,196,154,
101, 59,217,135,  4, 90,184,230,167,249, 27, 69,198,152,122, 36,
248,166, 68, 26,153,199, 37,123, 58,100,134,216, 91,  5,231,185,
140,210, 48,110,237,179, 81, 15, 78, 16,242,172, 47,113,147,205,
17, 79,173,243,112, 46,204,146,211,141,111, 49,178,236, 14, 80,
175,241, 19, 77,206,144,114, 44,109, 51,209,143, 12, 82,176,238,
50,108,142,208, 83, 13,239,177,240,174, 76, 18,145,207, 45,115,
202,148,118, 40,171,245, 23, 73,  8, 86,180,234,105, 55,213,139,
87,  9,235,181, 54,104,138,212,149,203, 41,119,244,170, 72, 22,
233,183, 85, 11,136,214, 52,106, 43,117,151,201, 74, 20,246,168,
116, 42,200,150, 21, 75,169,247,182,232, 10, 84,215,137,107, 53
};
//计算字节数组的8位签名
//灵感来自：https://github.com/WasatchPhotonics/CRC8_Example
公共字节计算CRC 8（字节[]数据数组，整数长度）
{
字节CRC=0；//初始值始终为0
for（int i=0；i字节b=（字节）（（n&（1CRC-8
有八位代表输入位字符串的签名：

您的实验可以是生成所有可能的长度为n
的2^n
不同输入位字符串，并注册导致给定签名的所有字符串
请注意，每次实验都必须从相同的初始8位状态字开始
您的示例输入长度为16位。有2^16=65536
不同的16位字符串。请分别尝试，找出哪些字符串与您的输入具有相同的签名
要了解CRC-8
电路的操作，请查看一个在线提供的动画CRC计算器。您还可以查看上的维基百科文章

使用C程序（见下文），我完成了这个实验。
无论输入位字符串的顺序如何（从左到右，反之亦然），65536位字符串中的256位具有相同的签名。我们可以从8位哈希方法中期待更多，它只提供256个不同的签名
我的代码：
using System;

namespace akCrc8Eval
{
    class Crc8Evaluator
    {
        // CRC 8 lookup table
        // https://github.com/WasatchPhotonics/CRC8_Example
        private static byte[] CRC_8_TABLE =
            {
              0, 94,188,226, 97, 63,221,131,194,156,126, 32,163,253, 31, 65,
            157,195, 33,127,252,162, 64, 30, 95,  1,227,189, 62, 96,130,220,
             35,125,159,193, 66, 28,254,160,225,191, 93,  3,128,222, 60, 98,
            190,224,  2, 92,223,129, 99, 61,124, 34,192,158, 29, 67,161,255,
             70, 24,250,164, 39,121,155,197,132,218, 56,102,229,187, 89,  7,
            219,133,103, 57,186,228,  6, 88, 25, 71,165,251,120, 38,196,154,
            101, 59,217,135,  4, 90,184,230,167,249, 27, 69,198,152,122, 36,
            248,166, 68, 26,153,199, 37,123, 58,100,134,216, 91,  5,231,185,
            140,210, 48,110,237,179, 81, 15, 78, 16,242,172, 47,113,147,205,
             17, 79,173,243,112, 46,204,146,211,141,111, 49,178,236, 14, 80,
            175,241, 19, 77,206,144,114, 44,109, 51,209,143, 12, 82,176,238,
             50,108,142,208, 83, 13,239,177,240,174, 76, 18,145,207, 45,115,
            202,148,118, 40,171,245, 23, 73,  8, 86,180,234,105, 55,213,139,
             87,  9,235,181, 54,104,138,212,149,203, 41,119,244,170, 72, 22,
            233,183, 85, 11,136,214, 52,106, 43,117,151,201, 74, 20,246,168,
            116, 42,200,150, 21, 75,169,247,182,232, 10, 84,215,137,107, 53
        };

        // Calculate 8-bit signature for byte array
        // inspired by:  https://github.com/WasatchPhotonics/CRC8_Example
        public byte Calc_CRC_8(byte[] DataArray, int Length)
        {
            byte CRC = 0;  //  initial value always 0

            for (int i = 0; i < Length; i++)
            {
                CRC = CRC_8_TABLE[CRC ^ DataArray[i]];
            }

            return CRC;
        }

        // Calculate 8-bit signature for 16-bit unsigned int
        private byte Calc_CRC_8(UInt16 n)
        {
            const int DIM = 16;
            byte CRC = 0;  //  initial value always 0

            for (int i = 0; i < DIM; i++)
            {
                byte b = (byte)(((n & (1 << i)) == 0) ? 0 : 1);
                CRC = CRC_8_TABLE[CRC ^ b];
            }

            return CRC;
        }

        public void getBitStringsWithSameSignature(byte[] bytes)
        {
            byte sig = Calc_CRC_8(bytes, bytes.Length);
            int count = 0;

            for (int n = 0; n < UInt16.MaxValue; n++)
            {
                if (sig == Calc_CRC_8((UInt16)n))
                {
                    count++;
                }
            }

            Console.WriteLine($"Found {count} bit-strings with signature {sig}");
        }
    }
}

使用系统；
命名空间akCrc8Eval
{
类Crc8Evaluator
{
//CRC 8查找表
// https://github.com/WasatchPhotonics/CRC8_Example
专用静态字节[]CRC_8_表=
{
0, 94,188,226, 97, 63,221,131,194,156,126, 32,163,253, 31, 65,
157,195, 33,127,252,162, 64, 30, 95,  1,227,189, 62, 96,130,220,
35,125,159,193, 66, 28,254,160,225,191, 93,  3,128,222, 60, 98,
190,224,  2, 92,223,129, 99, 61,124, 34,192,158, 29, 67,161,255,
70, 24,250,164, 39,121,155,197,132,218, 56,102,229,187, 89,  7,
219,133,103, 57,186,228,  6, 88, 25, 71,165,251,120, 38,196,154,
101, 59,217,135,  4, 90,184,230,167,249, 27, 69,198,152,122, 36,
248,166, 68, 26,153,199, 37,123, 58,100,134,216, 91,  5,231,185,
140,210, 48,110,237,179, 81, 15, 78, 16,242,172, 47,113,147,205,
17, 79,173,243,112, 46,204,146,211,141,111, 49,178,236, 14, 80,
175,241, 19, 77,206,144,114, 44,109, 51,209,143, 12, 82,176,238,
50,108,142,208, 83, 13,239,177,240,174, 7