Golay code refinements?

Question

Programming

Good afternoon, the question is, you need to implement the encoding and decoding of the Golay code. There are a couple of questions:

1. Let's say I entered the string " to1 ", in the Haming code, you need to take two characters and add control bits. But how to be in my case to encode one character at a time, adding not 11, but 15 zeros? That is, I represent the characters in binary form asci codes ( m = 11110010) ( o = 11101110), ( 1 = 11111)
   And I start to encode, in turn, each character: But in order to start encoding, I need to supplement the character up to 12 characters, but how write zeros in front or behind?
   It’s just that on the site on which I’m looking at the algorithm, they generally invert the number (the site at the end will throw off and screen)
   
2. 2) You need to do "exclusive or" in the algorithm it is written 11 times, but on the same site they do 5, and in the code in general 12 @[email protected]
   

It would be great if someone described the encoding and decoding algorithm point by point, using the same example "to1", otherwise I just got confused.
Thank you.
www.aqdi.com/golay.htm

Answer 1

1. You need to divide the character in half. Those. each character is a sequence of 8 bits. 3 characters -- 24 bits.
2. Before doing anything here, it's worth putting a few basic things from algebra in your head. You need groups, rings, finite fields, ideals. Think especially carefully about how the finite field F_2 and F_2^n are implemented, as well as the polynomial ring over the field F_2.