实验三CRC校验一、CRC校验码的基本原理编码过程：CRC校验码的编码方法是用待发送的二进制数据t(x)除以生成多项式g(x)，将最后的余数作为CRC校验码。
其实现步骤如下：1 设待发送的数据块是m位的二进制多项式t(x)，生成多项式为r阶的g(x)。
在数据块的末尾添加r个0，数据块的长度增加到m+r位。
2 用生成多项式g（x）去除，求得余数为阶数为r-1的二进制多项式y(x)。
此二进制多项式y(x)就是t(x)经过生成多项式g(x)编码的CRC校验码。
3 将y(x)的尾部加上校验码，得到二进制多项式。
就是包含了CRC校验码的待发送字符串。
解码过程：从CRC的编码规则可以看出，CRC编码实际上是将代发送的m位二进制多项式t(x)转换成了可以被g(x)除尽的m+r位二进制多项式所以解码时可以用接收到的数据去除g（x），如果余数位零，则表示传输过程没有错误；如果余数不为零，则在传输过程中肯定存在错误。
许多CRC的硬件解码电路就是按这种方式进行检错的。
同时,可以看做是由t（x）和CRC校验码的组合，所以解码时将接收到的二进制数据去掉尾部的r位数据，得到的就是原始数据。
解码过程示例：运行结果：附录（实现代码）：using System;using System.Collections.Generic;using System.Text;namespace CRC{public abstract class Change{/// <summary>/// 字节数组转进制/// </summary>/// <param name="bytes">字节数组</param>/// <param name="b1">字节数组长度</param>public static string ByteToHex(byte[] bytes, int b1){string returnStr = "";if (bytes != null){for (int i = 0; i < b1; i++){returnStr += bytes[i].ToString("x2").ToUpper();} }return returnStr;}/// <summary>/// 16进制转字节数组/// </summary>/// <param name="hexStr">16进制数</param>public static byte[] HexToByte(string hexStr){hexStr = hexStr.Replace(" ", "");if ((hexStr.Length % 2) != 0)hexStr += " ";//空格byte[] bytes = new byte[hexStr.Length / 2];for (int i = 0; i < bytes.Length; i++){bytes[i] = Convert.ToByte(hexStr.Substring(i * 2, 2), 16);} return bytes;}/// <summary>/// 字符串转进制/// </summary>/// <param name="str">字符串</param>/// <returns></returns>public static string StrToHex(string str){if (str == "") return "";byte[] bTemp = System.Text.Encoding.Default.GetBytes(str);return ByteToHex(bTemp, bTemp.Length);}/// <summary>/// 16进制转字符串/// </summary>/// <param name="str">16进制</param>/// <returns></returns>public static string HexToStr(string str){byte[] bytes = new byte[str.Length];bytes = HexToByte(str);return Encoding.Default.GetString(bytes);}}}namespace CRC{//哈夫曼树150// 结点类Node的定义如下：public class Node{private int weight; //结点权值private int lChild; //左孩子结点private int rChild; //右孩子结点private int parent; //父结点//结点权值属性public int Weight{get{return weight;}set{weight = value;}}//左孩子结点属性public int LChild{get{return lChild;}set{lChild = value;}}//右孩子结点属性public int RChild{get{ return rChild;}set { rChild = value; } } //父结点属性public int Parent{ get{ return parent; }set {parent = value; } } //构造器public Node(){weight = 0;lChild = -1;rChild = -1; parent = -1; }//构造器public Node(int w, int lc, int rc, int p){weight = w;lChild = lc;rChild = rc;parent = p;}}public class HuffmanTree{private List<Node> data = new List<Node>(); //结点数组private int leafNum; //叶子结点数目//索引器public Node this[int index]{get{return data[index];}set{data[index] = value;}}//叶子结点数目属性public int LeafNumpublic int LeafNum{get{ return leafNum;set{ leafNum = value; } }//构造器public HuffmanTree(){ }public HuffmanTree(List<NumKindchar> m_NumKind){leafNum = m_NumKind.Count;for (int j = 0; j < 2 * m_NumKind.Count - 1; j++)//n中字符共需要2n-1个节点{Node databuff = new Node();if (j < this.leafNum){databuff.Weight = m_NumKind[j].num; }data.Add(databuff);//每创建一个节点将节点加入节点数组data当中} }public List<Node> Create(){int max1, max2, tmp1, tmp2;//处理n个叶子结点，建立哈夫曼树for (int i = 0; i < this.leafNum - 1; ++i){ max1 = max2 = Int32.MaxValue;tmp1 = tmp2 = 0;//在全部结点中找权值最小的两个结点for (int j = 0; j < this.leafNum + i; ++j){ if ((data[j].Weight < max1) && (data[j].Parent == -1)){ max2 = max1;tmp2 = tmp1;tmp1 = j;max1 = data[j].Weight; }else if ((data[j].Weight < max2) && (data[j].Parent == -1)){ max2 = data[j].Weight;tmp2 = j;} }data[tmp1].Parent = this.leafNum + i;data[tmp2].Parent = this.leafNum + i;data[this.leafNum + i].Weight = data[tmp1].Weight + data[tmp2].Weight;data[this.leafNum + i].LChild = tmp1;data[this.leafNum + i].RChild = tmp2;}return data; }}public class NumKindchar{ public char letter { get; set; }//字符public int num { get; set; }//字符出现的次数public List<bool> huffmancode { get; set; }//字符对应的huffman编码}public class codeChar{public char numChar { get; set; }public string codeCharater { get; set; }}}。