Talk:Singleton bound

Statement of bound

This article does not state the Singleton bound in its most common and useful form. Most coding text books -- and, notably, Singleton's original paper itself -- states the Singleton bound as a bound on d, usually in the form d <= n-k+1, not as a bound on A_q(n,d). This article is unnecessarily opaque. — Preceding unsigned comment added by 128.149.22.213 (talk) 16:38, 1 April 2014 (UTC)

The version you refer to is only valid for linear codes (k is the dimension of the code) and follows immediately from the more general version which is called Singleton's bound in modern treatments. What is missing in this article is the simple derivation of the linear code form from the other, which I'll put in along with some other fixes. Bill Cherowitzo (talk) 03:40, 2 April 2014 (UTC)

Proof

I feel like that instead of this:

$|C|\leq A_{q}(n,d)\leq q^{n-d+1}.$

The proof needs something more like this:

$A_{q}(n,d)=|C|\leq q^{n-d+1}.$

Or am I missing something in the proof? 82.53.62.96 (talk) 16:42, 12 January 2012 (UTC) Damix

Introduction

It looks to me as if the size r is never used in the text. Maybe it shouldbe removed from the first sentence. Feynman81 (talk) 17:38, 16 March 2012 (UTC)