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You can use this info and code: Hamming(8,4) with Arduino.

There's a PDF with documentation about the process of creating a class that implements hamming(8,4) and a link to the source code.

You can use any class that derives from Stream (like Serial or SoftwareSerial).

Edit: If you want to implement a Hamming ECC in a Arduino it would be useful to precompute all the possible message values (you'll find more info at the link above). In a Hamming(8,4) your message is 1byte = 4bits + parity 4 bits; so you must divide your bytes in nibbles. It would be better to put all that stuff (code, decode, manage the upper/lower part of the byte, etc...) in a class. An example using the Hamming class from the link above:

Tx:

#include <hamming.h>

Hamming hamming(&Serial);
char message[] = "Hello World!!";

void setup()
{
  Serial.begin(9600);
  delay(100);
}


void loop()
{
  hamming.write(message);
  delay(1000);
}

Rx:

#include <hamming.h>

Hamming hamming(&Serial);
char message[Hamming::SIZE];

void setup()
{
  Serial.begin(9600);
  delay(100);
}

void loop()
{
  if(hamming.isMessageReady())
  {
    hamming.read(message);
    Serial.println(message);
  }
}

If you need to send other kind of info: a float, integer... you can do it, but I think it's a better idea to tokenize/detokenize your information and handle it like a "string".

P.S. You can use any kind of physical layer insofar as it's a child of Stream: Serial, SoftwareSerial...But I've only tested over Serial.