TWJ's profile - activity

thank you very much @selelivere

i have a vector $(x_1, \dots,x_n)$ where $x_i$ belongs to some set $E$ how can i assign randomly a letter $a,b,c$ to each vector than update it following some rule these vector ?

Example $E={ x_1, x_2,x_3 }$

$(x_1, x_2,x_3)=a$

$(x_2,x_3,x_1)=a$

$(x_3,x_1,x_2)=c$

$(x_3,x_2,x_1)=whatever$

$(x_1,x_1,x_1)=whatevre$ etc...

i have a rule that if $(x_1, x_2,x_3)=a$ and $(x_2,x_3,x_1)=a$ then $(x_3,x_1,x_2)$ must be equal to $a$

thank for your respond . this is the smallest non trivial example i cam with C is a BCH code over GF(4) `K.= GF(4);

R.<x>=K[]; V=x^3+x^2+a*x+a+1; V.is_primitive(); #yes L. = K.extension(V); g=1 #juse inisialzation for i in [1..28]: #the biggest delta(=28 here) the biggest g ==> the smallest our code c=b^(i) g=lcm(g,c.minpoly()) C = codes.CyclicCode(generator_pol = g, length = 63) C;`

say i have a cyclic code $C$ of length $n$ over a field $\mathbb{F}_{q^m}$ . is it possible to have construct a code $D$ of length $mn$ over $\mathbb{F_q}$

it's mathematically possible since $\mathbb{F}_{q^m}$ is a vector space of degree $m$ over $\mathbb{F}_q$

but i didn't find how to-do it in sage

thanks in advance

https://rua.ua.es/dspace/bitstream/10045/27320/1/Tesis_Diaz_Cardell.pdf (link text) can you please check Theorem 3.3 in page 51

Hi,

let $U$ be a square matrix of order $m$ over $\mathbb F_{q}$, more precisely $U$ is the companion matrix of a monic irreducible polynomial over $\mathbb F_{q}$ that define $\mathbb F_{q^m}$ .

let $\alpha$ be a primitive element of $\mathbb F_{q^m}$

I wish to declare this morphism to compute some examples with SAGEMATH

$\psi$: $\mathbb F_{q^m}$ $\rightarrow$ $\mathbb{F}_{q}[U]$

$\alpha$ $\mapsto$ $\psi(\alpha)=U$

thanks in advance;

i apologize for the formatting , ididn't know that LaTeX won't compile

as concern the matrix U is defined over 𝔽q in fact it's the companion matrix of the irreducible polynomial that we used to construct 𝔽qm so if α is a primitive element of 𝔽qm ψ(α)=U ψ(α²)=U² etc,,,

Hi, let $U$ be a squar matrix of order $m$ , I wish to declair this morphismes to compute some examples with SAGEMATH

{\begin{tabular}{ccc} $\psi: \mathbb{F}_{q^m}$ & $\rightarrow$ & $\mathbb{F}_{q}[U]$ \ $\alpha$ & $\mapsto$ & $\psi(\alpha)=U $\ \end{tabular} }

and this one

{\begin{tabular}{ccc} $\Psi: \mathcal{M}(\mathbb{F}_{q^m})$ & $\rightarrow$ & $\mathcal{M}(\mathbb{F}_{q}[U])$ \ $\mathcal{A}=[a_{i,j}]$ & $\mapsto$ & $\Psi(\mathcal{A})=[\psi(a_{i,j})] $\ \end{tabular} }