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2018-05-10 06:31:13 -0500 commented answer convert a cyclic code $C$ of length $n$ over a field $\mathbb{F}_{q^m}$ to a code $D$ of length $mn$ over $\mathbb{F_q}$

thank you sir although i still trying to understand what the last loop dose , i have tow observation

the lifted of the generator matrix of a code isn't always the generator matrix of the lifted code. for example the code $C=(0,0)(1,\alpha)(\alpha,\alpha+1)(\alpha+1,1)$ is generated by $(1,\alpha)$ " a 1*1 matrix by the lifted code $D=(0,0,0,0)(1,0,0,1)(0,1,1,1)(1,1,1,0)$ is not generated by $(1,0,0,1)$ the lift of $(1,\alpha)$

my second observation is that $C$ and $D$ should have the same cardinal since we are replacing every codeword by a codeword with twice it length

however, i believe i can use the function get_lift() that you defined and apply it t every codeword in $C$ and store the result somehow in $D$ .

i again ... (more)

2018-05-09 05:35:02 -0500 commented question convert a cyclic code $C$ of length $n$ over a field $\mathbb{F}_{q^m}$ to a code $D$ of length $mn$ over $\mathbb{F_q}$

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;`
2018-05-08 12:24:06 -0500 received badge  Scholar (source)
2018-05-08 12:17:21 -0500 asked a question convert a cyclic code $C$ of length $n$ over a field $\mathbb{F}_{q^m}$ to a code $D$ of length $mn$ over $\mathbb{F_q}$

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

2018-03-19 08:08:58 -0500 commented question (how/can) i declair this isomorphism

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

2018-03-17 02:32:52 -0500 received badge  Editor (source)
2018-03-16 18:53:34 -0500 asked a question (how/can) i declair this isomorphism

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;

2018-03-15 07:30:36 -0500 commented question (how/can) i declair this isomorphism

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,,,

2018-03-08 01:55:14 -0500 asked a question (how/can) i declair this isomorphism

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} }