# Talk:Block design

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Field: Discrete mathematics
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## 1

I'd be grateful if anyone could explain why 'partial incomplete block design' is the terminology could add that.

Charles Matthews 19:48, 19 Nov 2004 (UTC)

In full, "balanced incomplete block design". "Incomplete" because you don't use all k-element subsets. "Balanced" because every pair of elements (I'm referring to the main original designs, which were 2-designs) is in the same number of blocks. Zaslav 11:54, 26 February 2007 (UTC)

## 2

I plan to move "T-design" back to "Block design". Please do not move it back to "T-design" (or "t-design"). The general term is "block design" or in full "balanced incomplete block design". A particular kind of block design is called a t-design. (The t, properly speaking, is a number.) The conventions of the field make the term "block design" the best one for an article (unless you prefer the long name, which is not as much used nowadays). I am open to being shown wrong on this, but my experience indicates that's what experts would say. Zaslav 10:52, 26 February 2007 (UTC)

Moved. Again, I ask people not to move this back to "T-design" without deep thought. If you object, let's discuss it and decide. Zaslav 11:57, 26 February 2007 (UTC)

## confusion

As usual with stuff concerning graph theory/combinatorics, conventions differ. in my syllabus it saids every 2-design is a block and vice versa

But more importantly , it says : $S_{\lambda} (t , k, v)$ is a t-design , when :

• the number of points is v
• the number of points on a line is k
• through every subset of the point set with t elements there are \lambda blocks

now the r defined here , is the number of blocks through one point x now some basic counting teaches me immediately :

${v-1 \choose t-1} \lambda= r {k-1 \choose t-1}$

My syllabus apparently backs me up on this formula. My question, why should this be included in the definition when it is abundant as it (apparently) can be calculated immediately from the rest

My apologies if I am wrong, I am just a student and most of maths is still new to me, but I am very busy with it all.

Kind regards, Evilbu 16:58, 15 February 2006 (UTC)

You meant "redundant", of course. The reason r is in the notation (not definition, though it could also be in the definition) is that it's important to know. Another notation is "t-(b,v,r,k,λ) design", the b and r being predictable from the rest, but important to know. The reason they're important is that they have to do with the size of the design, which matters when you have to pay for it. (This notation suggests why one says "2-design" or "t-design"; the t was an afterthought, originally, since t = 2 was the main topic at first.) Zaslav 10:58, 26 February 2007 (UTC)

## Coding-theoretic applications missing

Currently, the article is "purely" Design-theoretic and is lacking a Coding Theory perspective. A case, for example, is an error-correcting code whose codewords are the lines of a symmetric (v,k,λ)-design. If I'm not mistaken this is what is called a Balanced incomplete block design code.
Omnipedian (talk) 14:24, 26 November 2008 (UTC)