This page maintained by Neil J. A. Sloane.
Address: AT&T Shannon Lab, 180 Park Ave, Room C233,
Florham Park NJ 07932-0971 USA
Voice: 973 360 8415,
Fax: 973 360 8178.
Email: njas@research.att.com
This book first appeared in 1977 and the 10th impression was printed in 1998.
North-Holland/Elsevier keep asking for a revision, but this will be an immense task, and so will not happen for a good while.
They have finally corrected my date of birth (on page iv), which was correct in the first edition, but in later printings was given as 1039- , making me the oldest living North-Holland author.
The book should be ordered directly from the publisher. Details: ISBN: 0-444-85193-3, 762 pp., North-Holland Mathematical Library, Volume 16. Publisher: North-Holland, New York; Elsevier Science Publishers B. V., P.O. Box 103, 1000 AE Amsterdam, Netherlands, Tel.: +31 (20) 485 2610, Fax: +31 (20) 485 2616 To go to their web site, click here.
I have heard many complaints that the book is always missing from libraries, out of print at the publisher, and so on. It should be in print now. In case of difficulty, contact Drs. Arjen Sevenster, Associate Publisher, Elsevier Science Publishers, Sara Burgerhartstraat 25, 1014 AG P.O. Box 103, 1000 AE Amsterdam, Netherlands, a.sevenster@elsevier.nl, fax: 01-31-20-485-2616.
Scattered through my notes and files are numerous
corrections that need to be made.
Any that I come across from now on will be added to the following list.
In Chapter 16, paragraph 4, Theorem 8 (ii) (on p. 490) no restriction on $p$ is made, but the proof uses Theorem 7 which requires $p\equiv3\pmod{4}$.- Markus Grassl (grassl@ira.uka.de), Aug 3, 2000
In Chapter 11, paragraph 5, Theorem 9 has to be slightly modified.- Markus Grassl (grassl@ira.uka.de), May 28, 2002The current version reads:
For any k, 1<=k<=q+1, there exists a [q+1,k,q-k+2] cyclic MDS code over GF(q)
This is false for q odd and k even. Then "cyclic" has to be replaced by "constacylic". The proof in the book deals only with even characteristic. For odd characteristic, the polynomial X^(q+1)-1 has two linear factors (X-1) and (X+1) over GF(q). This makes it impossible to have a generator polynomial of even degree and consecutive zeroes.
Instead of X^(q+1)-1, one can use the polynomial g(X)=X^(q+1)-w where w is a primitive element of GF(q).
If alpha denotes a primitive (q+1)-th root of unity (over GF(q^2)) and v denotes a primitive element of GF(q^2), G(X) has the conjugated roots
v*alpha^i and v*alpha^(1-i)
(as v is an (q+1)-th root of w).
Taking the products of the polyomials (x-v*alpha^i)*(x-v*alpha^(1-i)) as generator polynomial of the constacyclic code yields the desired result.