How Do You Construct a [4, 7^2, 3] Code Using MOLS?

  • Context: Graduate 
  • Thread starter Thread starter SomeRandomGuy
  • Start date Start date
  • Tags Tags
    Coding Homework Theory
Click For Summary

Discussion Overview

The discussion revolves around the construction of a [4, 7^2, 3] code using mutually orthogonal Latin squares (MOLS). Participants explore the implications of the notation, the requirements for constructing the code, and the relationship between MOLS and the code's parameters.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant asserts that a [4, 7^2, 3] code exists due to the prime nature of 7, suggesting there are 6 MOLS available for construction.
  • Another participant questions the feasibility of encoding 49 symbols in a codeword of only 4 symbols, expressing uncertainty about the acronym MOLS.
  • A participant clarifies that MOLS stands for mutually orthogonal Latin squares and speculates that the notation refers to a 3-error correcting code with 7^2 codewords of length 4.
  • There is a suggestion that the construction might yield codewords of length 8, and a question is raised about whether the original poster is struggling with producing MOLS or constructing the code from them.
  • One participant confirms the understanding of the notation and explains that the minimum distance refers to the separation between codewords, which simplifies the construction process by requiring only 2 MOLS instead of 6.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the construction of the code and the implications of the notation. There is no consensus on the best approach to constructing the code, and some uncertainty remains about the requirements and definitions involved.

Contextual Notes

There are unresolved assumptions regarding the definitions of MOLS and the parameters of the code, as well as the implications of the minimum distance on the construction process.

SomeRandomGuy
Messages
55
Reaction score
0
Construct a [4, 7^2, 3] code. I know it exists because 7 is prime, so there are 6 MOLS. However, I am not quite sure how to go about constructing this code.
 
Physics news on Phys.org
You sure you have that right? You can't encode 49 symbols in a codeword that's only 4 symbols long.

I don't know the acronym `MOL' either.


This sounds like a homework question -- you can usually metareason these out: it would probably be done using a code (or a technique) that you learned recently.
 
MOLS=mutually orthogonal latin squares

I'm not positive what the (4,7^2,3) notation refers to, I'm guessing a 3-error correcting code with 7^2 codewords of length 4 (7 symbols each position?).

The construction I have in mind would make codewords of length 8 though. This is a pretty standard construction, and assuming it's what you're trying to do: are you having problems producing the MOLS or coming up with the code given a set of 6 MOLS? (or both?)
 
shmoe said:
MOLS=mutually orthogonal latin squares

I'm not positive what the (4,7^2,3) notation refers to, I'm guessing a 3-error correcting code with 7^2 codewords of length 4 (7 symbols each position?).

The construction I have in mind would make codewords of length 8 though. This is a pretty standard construction, and assuming it's what you're trying to do: are you having problems producing the MOLS or coming up with the code given a set of 6 MOLS? (or both?)

Yes, MOLS is mutually orthogonal latin squares. the notation (4, 7^2, 3) referes to an [n, M, d] code where n is the length of each vector in the code, M is the number of vectors, and d is the minimum distance between them.

Anyway, I figured it our, so it's all good. Thanks for the responses.
 
SomeRandomGuy said:
Yes, MOLS is mutually orthogonal latin squares. the notation (4, 7^2, 3) referes to an [n, M, d] code where n is the length of each vector in the code, M is the number of vectors, and d is the minimum distance between them.

Anyway, I figured it our, so it's all good. Thanks for the responses.

ahh, 3 being minimum distance and not the level of error correction would explain how length 4 code words will be sufficient. Much simpler to construct the code when you only need 2 MOLS and not 6!
 

Similar threads

Graduate Have I solved this iterative equation correctly?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Looking for a creative or quick method for finding roots in GF(p^n)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Trouble understanding an online solution to an exercise in Dummit & Foote
  • · Replies 21 ·
Replies
21
Views
2K
How do I connect a button pressed signal with code in Godot 4?
  • · Replies 1 ·
Replies
1
Views
7K
Undergrad Questions about non existence of GCDs vs (coimages, cokernels)
  • · Replies 12 ·
Replies
12
Views
1K
Constructing K-Maps & Gray Codes w/ 2, 3 & 4 Bits
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How do I find the change of basis matrix for the JCF of M?
  • · Replies 6 ·
Replies
6
Views
2K
C/C++ Puzzle with C++ constructor and overloaded operator
  • · Replies 23 ·
Replies
23
Views
3K
MHB How Do You Calculate the Total Weight of a Huffman Code?
  • · Replies 1 ·
Replies
1
Views
1K
Engineering Total Lateral Stiffness from Stiffness Matrix
  • · Replies 0 ·
Replies
0
Views
2K