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 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, $I_0^2$? added 10 characters in body 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 $GF((2^2)^3)$? deleted 4 characters in body