A note on binary cyclic codes of blocklength 63

✍ Scribed by Richard E. Blahut

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 508 KB
• Volume: 106-107
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90527-m

✦ Synopsis

A method of investigating the minimum distance of binary cyclic codes of composite blocklength is described; only the case of blocklength 63 is discussed in any detail. Moreover, the usefulness of the method is left as an unanswered question.

'Your proof of Theorem 5.9.2 is the same as the one in MacWilliams-Sloane and I claim that it is incorrect. It is necessary to show that c(x)E(x) is not 0 and to do this, one must know that d* is odd. That is the hard part of the square root bound.'

Since this was not my first mistake in life, I reacted by hoping that not too many others would notice it, but it gave me a problem when I began to think about a second edition of the book. The standard way to close the gap that van Lint showed me is to use the Gleason-Prange theorem but I could find no published proof of that theorem that suited my peculiar taste and style.