There is no single text book for the course yet. There are many many
textbooks aimed at different audiences. Here is a list of some books
that are known to me.
1. The theory of error-correcting codes by F.J. MacWilliams and
N.J.A. Sloane, North-Holland.
A great thick book, a classic.
2. A first course in coding theory by Raymond Hill, Oxford.
A good introduction
3. Introduction to the theory of error-correcting codes
by Vera Pless, third ed., Wiley.
4. Coding Theory San Ling and Chaoping Xing, Cambridge Univ. Press.
A good book, came out recently. about 45 bucks.
5. Algebraic Coding Theory by E. Berlekamp, McGraw Hill.
Another classic.
6. The theory of information and coding by E. McEliece, Cambridge.
A fairly recent book by a leader of the field.
7. Modern Coding Theory by T. Richardson and R. Urbanke, Early copy available Online for
free!! and frequently updated.
8. Introduction to Coding Theory by J.H. van Lint, second edition,
Springer Verlag.
An excellent book. A very mathematical treatment.
9. Introduction to Coding Theory by Ron Roth, Cambridge, 2006.
10. Algebraic-Geometry Codes by M. Tsfasman and S. Vladut, Kluwer.
11. Claude Shannon's original monumental paper
A Mathematical Theory of Communication