List questions from coding-theory

Published on 14 Mar 2018 - 10:05

1.2k

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Max Hamming distance given n

Published on 22 Mar 2026 - 4:22

264

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Error correction for short strings

Published on 21 Mar 2026 - 22:37

61

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Difference between $F_2^n$ and $\Bbb F_2^n$ for a field

Published on 14 Mar 2018 - 20:06

186

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Show that every word of weight $4$ in $\mathbb{F}_{2}^{23}$ is of distance $3$ from exactly one codeword in the binary Golay code $G_{23}$.

Published on 17 Mar 2018 - 11:46

249

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If a binary $(n,M,d)$ code with $d$ even exists, then exists an $(n,M,d)$ code with even weight for all it's codewords

Published on 20 Mar 2018 - 2:23

426

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Design the best schemes in terms of information transmission speed

Published on 20 Mar 2018 - 13:52

120

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Are there explicit constructions of codes attaining the GV bound?

Published on 20 Mar 2018 - 17:47

91

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An Extension of an $MDS$ Code

Published on 21 Mar 2018 - 22:29

172

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Prove that the repetition code is the only linear code with parameters $[n,1,n]$

Published on 22 Mar 2018 - 5:03

1.8k

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How 8th bit in [8;4] Hamming code works?

Published on 22 Mar 2018 - 12:56

37

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Prove $p=2$ for a linear $[p^m+2, p^m-1, 4]$ MDS code

Published on 23 Mar 2018 - 6:30

178

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What happen when a lattice is contained in its dual?

Published on 23 Mar 2026 - 8:46

702

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Seeing weight of a code from generator matrix

Published on 22 Mar 2026 - 14:47

74

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How many cyclic codes are there containing $g(x)$?

Published on 26 Mar 2018 - 16:27

List Question

Group theory / codes

Max Hamming distance given n

Error correction for short strings

Difference between $F_2^n$ and $\Bbb F_2^n$ for a field

Show that every word of weight $4$ in $\mathbb{F}_{2}^{23}$ is of distance $3$ from exactly one codeword in the binary Golay code $G_{23}$.

If a binary $(n,M,d)$ code with $d$ even exists, then exists an $(n,M,d)$ code with even weight for all it's codewords

Design the best schemes in terms of information transmission speed

Are there explicit constructions of codes attaining the GV bound?

An Extension of an $MDS$ Code

Prove that the repetition code is the only linear code with parameters $[n,1,n]$

How 8th bit in [8;4] Hamming code works?

Prove $p=2$ for a linear $[p^m+2, p^m-1, 4]$ MDS code

What happen when a lattice is contained in its dual?

Seeing weight of a code from generator matrix

How many cyclic codes are there containing $g(x)$?

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