Non-Binary Error Control Coding for Wireless Communication and Data Storage (Carrasco/Non-Binary Error Control Coding for Wireless Communication and Data Storage) || Algebraic-Geometric Codes

✍ Scribed by Carrasco, Rolando Antonio; Johnston, Martin

• Publisher: John Wiley & Sons, Ltd
• Year: 2008
• Weight: 536 KB
• Category: Article
• ISBN: 0470518197
• DOI: 10.1002/9780470740415.ch4

✦ Synopsis

P 0 = (0, 0), P 1 = (0, 1), P 2 = (1, α), P 3 = (1, α 2 ), P 4 = (α, α), P 5 = (α, α 2 ), P 6 = (α 2 , α) and P 7 = (α 2 , α 2 ).

Let the message polynomial be f (x, y) = 1 + y + x 2 . Then each coded symbol

Hence the code word is c = 1, 0, α 2 , α, 0, 1, 1, 0. This is also equivalent to multiplying a message vector m by a generator matrix G. To construct the rows of the generator matrix of an AG code, each monomial