nk block codes

[tec5c]

Sorry for posting in the wrong thread. "Desperate times call for desperate measures..."

I have a question in regards to (n,k) block codes. For a given value of k i.e., (n, 54) which is guaranteed to correct t=10 errors and L is an integer such that L >= n.
What is the numerical value for L?

I don't really understand what L is representing. My assumption is that n is the optimal value for bandwidth efficiency however L is acceptable just with some trade offs.

Is this assumption accurate?

Secondly, I have tried multiple approaches to finding the value of n (which I assume will be the value for L seeing as it can be equal to n). These include using the Plotkin bound, which resulted in the value for n being smaller than the given value of k. I've tried using the definition in the image below and using Matlab to solve the inequality, resulting in there being no value for n (?)



I'm not really sure how else to approach this question.

Am I missing something simple/obvious here? Any advice is greatly appreciated.

[tec5c]

Bump.

[Marco]

Lets google block code.

Lets try to find the part most likely needed to solve the problem :

"A code with distance d allows the receiver to detect up to d-1 transmission errors"

So we need d >= 11.

"For maximum distance separable codes, the distance is always d=n-k+1"

Now I'm going to make a small jump in logic which I think is plausible, but which I'm not going to prove because I'm far too lazy. I think it's logical that if we calculate n according to the above equation then for that value or higher values d >= 11 can be guaranteed.

So n >= 10+k, L >= n, so L >= 10+k.

I honestly don't see why L was even brought into it, but experience dictates it's just poor problem construction rather than anything meaningful.

[tec5c]

"A code with distance d allows the receiver to detect up to d-1 transmission errors"

So we need d >= 11.

If the code is guaranteed to correct t=10 errors, then d >= 11 does not seem correct.

Seeing as, d <= 2t + 1

So shouldn't d <= 21? Then continue on with your approach.

Then errors detected = 20.

Regardless, thank you for your reply.

[Marco]

BTW rather than invoking MDS for that equation it's probably better to say you are using the Singleton bound.

[tec5c]

BTW rather than invoking MDS for that equation it's probably better to say you are using the Singleton bound.

MDS?

Using the Plotkin bound was just one approach I had tried... Singleton appears to be the way to go.

[Marco]

Maximum Distance Separable codes.

[tec5c]

Ah yep. I see what you mean now.

Also, out of curiosity, do you work in the comms field? Or just a HAM or something?

[Marco]

No, just some deja vu from my college days.

[tec5c]

 Well you have some fine memory retention skills then 

Thanks for your help.