Talk:Singleton bound

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

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)

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)

Attribution

The article mentions that the bound was already obtained by Joshi (in 1958), who attributes it to Komamiya (in 1953) but with a more complicated proof. Welsh (1988) also attributes it to Komamiya. But actually in Joshi's paper, only has the statement for q=2 is stated and proved. The proof is basically the same of course, but I do not see why the general result should be attributed to Joshi. (For Komamiya, I do not have access to the paper. Joshi does not mention that it has a more general statement. Welsh presents the general statement and states that "it appears to go back to Komamiya" so I am not sure he had access to this paper.)

I propose to slightly modify the text to state that Joshi obtained the bound in the special case q = 2.

--B!Gre (talk) 13:52, 5 February 2026 (UTC)