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  • 31 votes cast
Oct
21
comment How do I prove that the following is a presentation of $\mathbb{Z_{35}}$?
Thank you so much for your detailed response. I will take my time to read carefully your answer, and write back if there were any questions. Thanks again.
Oct
21
asked How do I prove that the following is a presentation of $\mathbb{Z_{35}}$?
Sep
22
accepted How do I find a (7, 3) parity check code generator matrix?
Sep
21
comment How do I find a (7, 3) parity check code generator matrix?
I came up with another matrix using $p(x) =1+x+x^3+x^4$ $$G=\pmatrix{1&0&0&1&1&0&1\cr0&1&0&1&0&1&1\cr0&0&1&1&0&0&0\cr}$$ Would this also be correct? I'm confused about the polynomials one chooses and I didn't find any literature that I could understand addressing this problem.
Sep
21
awarded  Autobiographer
Sep
21
comment How do I find a (7, 3) parity check code generator matrix?
I 'll do that now. :) Thanks again.
Sep
21
comment How do I find a (7, 3) parity check code generator matrix?
Thanks for your answer. Would the explanation for how you came about constructing the matrix also be there?
Sep
21
asked How do I find a (7, 3) parity check code generator matrix?
Jul
28
comment Can an interval be represented as a set?
Yes, intervals are sets, $A_n = \{x \in \mathbb{R} : 0 \le x \le n\}$ and $A = \{x \in \mathbb{R} : x \ge 0\}$. You can apply the theorem previously proved.
Jul
25
revised Why are the sets $U_x$ disjoint in this proof of the non path-connectedness of the ordered square, $I_0^2$?
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Jul
25
comment Why are the sets $U_x$ disjoint in this proof of the non path-connectedness of the ordered square, $I_0^2$?
@BrianM.Scott Thanks for the correction. I'd forgotten exactly what it meant for a set to be well-ordered at the time.
Jul
24
answered Why are the sets $U_x$ disjoint in this proof of the non path-connectedness of the ordered square, $I_0^2$?
Jul
22
awarded  Yearling
Jul
22
comment Does anyone understand this proof: If $A$ is closed and bounded $\implies A$ is sequentially compact.
@BozoVulicevic $A$ is closed iff $x_n \in A$ and $x_n \to x$ implies $x \in A$.
Jul
22
answered Does anyone understand this proof: If $A$ is closed and bounded $\implies A$ is sequentially compact.
Jun
21
accepted How does one construct the Galois field extension $GF((2^2)^3)$?
Jun
21
comment How does one construct the Galois field extension $GF((2^2)^3)$?
Thank you for answering. I have a question, why is it that $-1 = 1$, when I was doing the calculations by hand yesterday, I was using $-3=1$, and I had $\beta^3=3 \alpha \beta^2 + 3\alpha \beta + 3 \alpha$. Also, how do you find the inverse of $\alpha$, and then how exactly does $\beta^4= \beta^2 + \beta + \alpha^2$? If you can help with the relations of the elements in the coefficient field, then I think I'll be able to do the calculations.
Jun
20
comment How does one construct the Galois field extension $GF((2^2)^3)$?
@JyrkiLahtonen I don't think we're being asked to check if the polynomial is indeed primitive. I don't know very much yet, but I'm thinking the problem is to write down/find explicitly every element of the finite field as a linear combination of the basis elements of the corresponding cyclic group when, say, $\beta$ is the primitive element. I tried doing that and after very tedious computations wasn't able to show that $\beta^{63}=1$.
Jun
20
comment How does one construct the Galois field extension $GF((2^2)^3)$?
@ZevChonoles Yes.
Jun
20
revised How does one construct the Galois field extension $GF((2^2)^3)$?
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