Recent content by sara15

Thanks for replying to my question. I do not know how to find the characteristic polynomial by this way (x-alpha)(x-sigma(alpha))...(x-sigma^n-1(alpha)) this is called the characteristic polynomial of alpha over Fq , where alpha is in Fq^n. and the primitive polynomial is a monic polynomial...

Hey guys, I really need some help please! I would really appreciate it if anyone can help out, if we have F16 = F2/(x^4+x+1). can anyone explain to me how can I compute the minimal polynomials and the characteristic polynomils over F2 of elements of F16 and to point out the primitive ones...

If we have N:F_q^n ...> F_q , be the norm function . can anyone explian how the map N is surjective .

can we define a V-sentence phi such that phi has arbitrarily large finite models and , for any finite model G , |G| is even . and then finding a finite graph G such that |G| is even and G doesnot model the sentence phi that I mentioned above. please explain it to me

yes it means a subgraph

If we have K_n denote the complete graph on n vertices, can anyone explain to me how to know how many substructures does K_n have?

how to define a V-sentence phi such that phi has aebitrarily large finite models and for any finite model G , G is a connected graph. after that to find a connected graph that does not model the sentence phi. please explain it to me.

can anyone give me a first-order sentence that says there exist exactly three elements. Please explain it to me. Thanks

ok I could get the generator matrix , but I still do not know how to find the parity check matrix and the minimum distance and then decode m1= 1100010 and m2 = 0111010 Many thanks Sara

Thank you very much

consider the binary encoding function that sends (a1,a2,a3) into (a1,a2,a3,a1+a2, a2+a3, a1+a3,a1+a2+a3). First , how can I give a generator matrix of this code . then how can I provide the parity check matrix , giving n,k and the minimum distance of the code. Finall, how to decode m1=1100010...