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Apr
19
comment Extended Golay codes are self dual
What definition do you have for Golay codes? The proof will depend on how you describe a Golay code.
Mar
31
comment Proving a subcode is cyclic.
What is an "even-like" vector?
Mar
25
comment Take the derivative of a Hamming Weight Enumerator
Hint: $iA_i$ equals the total number of $1$'s in all the codewords of weight $i$. So, $\sum_i iA_i$ is the total number of $1$s in _all_ $2^k$ codewords of the code. Now, instead of counting the $1$'s in each codeword and taking the total, count the number of $1$'s in each coordinate or bit position and take the total.
Mar
17
comment Let $X = \dfrac{1}{25} \sum\limits_{i=1}^{25} X_i$ and $Y =\dfrac{5}{2}X - \dfrac{2}{5}$. What is $P(|Y| > 1)$?
Why is $X \sim N(1,4)$, the same as all the $X_i$?
Mar
17
comment Cyclic code and its generating polynomial
Have you tried anything at all towards solving the problem yourself? Even something as trivial as making a list of all 8 binary vectors of length 3 before asking here?
Mar
9
comment Question about subfield subcode of a cyclic code
If all the symbols in a particular codeword are in the subfield, does this property hold for cyclic shifts of that codeword?
Mar
9
comment Question about subfield subcode of a cyclic code
math.stackexchange.com/q/1679500/15941 ?
Mar
8
revised Bivariate normal distribution $X$ and $Y$
added 13 characters in body
Mar
7
comment Decoding BCH code
The value of $e$ is determined during the decoding calculations. But in this case, it is obvious that $e=2$ because the code has minimum weight $5$ while the received vector has weight $3$.
Mar
7
comment Decoding BCH code
Why not read further on the Wikipedia page where it tells you that there are several different algorithms for determining $e$ and describes them in some detail?
Mar
7
comment Bivariate normal distribution $X$ and $Y$
"(since $X$ and $Y$ are independent)" No, they are not. They are correlated random variables.
Mar
7
comment Bivariate normal distribution $X$ and $Y$
I don't think the result is correct unless $X$ and $Y$ are standard normal to start with
Mar
4
comment Proof of Weak Law of Large Numbers using Chebyshev's Inequality
Why does $P(\mu-c<\bar{X}_n < \mu+c)$ equal the other stuff when $c$ is approaching $0$ but is not quite there yet?
Mar
4
comment Calculating a Weight Enumerator Polynomial for a Linear Code
If by $h$ you mean the dimension of the dual code, then the MacWilliams-Sloane book is as good a reference as any.
Mar
4
comment Construct generator polynomial with cyclotomic sets
I have no idea what you mean by $3$. Are you still doing arithmetic mod $31$? See the comments by @Jyrki on the main question. Also, read his incredibly detailed beautiful answer on a different question to understand the difference between $\mathbb F_{31}$ and $\mathbb F_{32}$. Until you stop using $\mathbb F_{31}$ as a substitute for $\mathbb F_{32}$, you will not be able to make any progress on this topic.
Mar
4
comment Calculating a Weight Enumerator Polynomial for a Linear Code
There are no simple algorithms (other than the brute-force enumeration you mentioned) that can be applied to all codes, but the weight enumerators of some codes can be found more easily by studying the code structure (or the dual code structure and applying the MacWilliams identities).
Mar
4
answered Construct generator polynomial with cyclotomic sets
Mar
3
comment Why is this system non-linear?
Yes, it is straightforward to show that the cascade is nonlinear over $\mathbb R$. That the output is not a linear function over $\mathbb F_2$ of the input is seen from the fact that the output is not even in $\mathbb F_2$.
Mar
3
answered Why is this system non-linear?
Feb
27
answered Difference of two Gamma random variables