# Questions tagged [coding-theory]

Use this tag for questions about source coding, error-correcting codes, error-detecting codes, and related algebraic and/or combinatoric constructions.

1,258 questions
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### Difference Entropy Output and Input [on hold]

In a ternary channel with same probabilities for all inputs. I have H(X) entrance entropy and H(Y) output entropy. What does the difference of these 2 Entropy tell me?
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### Majority voting 9 Bits Error probability

i have 1 Bit that will send 9 times. Each bit has an error probabiltiy of 1/3. The received Bits will be interpreted with a majority voting. Do anyone have an idea how i do check the probability ...
1answer
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### Parity check matrix H given; justify that C can correct one error, does a word belong to C and correct an error. [on hold]

I'm trying to learn about error correcting codes, and I have this question from a previous exam. Now I'm a little bit confused because I can't seem to wrap my head around this one, could I please get ...
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### VBA Macro and ActiveX Button Consolidation [on hold]

I have two Active X buttons that work and am trying to make one button that does both actions simulataneously. The first ActiveX button sorts through a data array and hides any rows that do not have ...
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### Product of generalised Reed-Solomon Codes

I know the definition of a generalised Reed-Solomon Code: $$GRS_{n,k} (\alpha, v) = \{(v_0 f(\alpha_0), ..., v_{n-1}f(\alpha_{n-1}) ): deg f < k \}.$$ I know also that the product of two GRS ...
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### Codes that maximize average minimum distance from any tuple?

Inspired by this question. I'd wish to know about binary codes that seek to maximize, not the distance from each codeword to the nearest codeword, but the average distance from any vector ($n-$tuple) ...
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### BCH code properties

I am a newbie in error correcting codes and interested to understand binary BCH codes. I understand that all the code words are at least in dmin = 2t+1 Hamming distance of each other. But I have the ...
1answer
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### construct parity check matrix from hamming code (3,4)

So I have this question. let $${F_4} = \{0, 1 , x, x^2 | x^2 = x + 1 \}$$ Use Ham(3,4), with a parity-checkmatrix having columns in lexicographical order, to decode (a) 1111111 1111111 1111111; (...
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### Construct parity-check matrix for HAM(3,4)

So I have this question. let $${F_4} = \{0, 1 , x, x^2 | x^2 = x + 1 \}$$ Use Ham(3,4), with a parity-checkmatrix having columns in lexicographical order, to decode (a) 1111111 1111111 1111111; (...
1answer
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### Parity check matrix for the Hamming code Ham(2,7)

I'm trying to figure out how to construct a parity check matrix for a Ham(2,7) where Ham(2,7) is Ham(r,q). I really don't understand where the columns of matrix come from my Text Book says to list all ...
2answers
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### Proving that there doesn't exist a binary code with parameters [6,5,4]

I'm new to code theory and I'm having trouble with proving if a code doesn't exist in general. I found a binary code with the parameters [6,4,4] but I don't really understand why there cant be one ...
2answers
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### How do I find $\bar{y}$ in this question?

A summary of $20$ observations of $y$ gave the following information $\sum(y-a)=-37$ $\sum(y-a)^2=1529$ Find the mean and standard deviation of $y$. In this question, I was able to ...
1answer
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### Rate of systematic code that is a combination of two codes over the same information symbols.

Let $I_k$ be the systematic columns and let two codes be defined over the same systematic columns $I_k$ as below. Let $[n_1,k]$ be the first linear systematic code with rate $\frac{k}{n_1} \leq r_1$,...
2answers
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### Idempotents and cyclic codes

Let $C_1 = \langle e_1(x) \rangle$, $C_2 = \langle e_2(x) \rangle$ cyclic codes, where $e_1(x)$ and $e_2(x)$ are idempotents. I know what cyclic codes and idempotents are, but why can one deduce the ...
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1answer
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### Error probability of repetition code

I am very lost. I would like to know how I calculate the probability of finding errors in repetition code. For example say the codewords are 111 or 000 and probability of an error is 0.1. How would I ...