What exactly is a linearized polynomial in field theory?

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I read the wikipedia article on Linearized polynomials.



But I'm not sure the quite use-case of it.



Can anyone elaborate on it?




field-theory finite-fields




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  • Can you explain better your question?
    – Taroccoesbrocco
    Aug 1 at 11:18










  • @Taroccoesbrocco what's linearized polynomial for? For example, when do we use that polynomial? Cryptography? Error Correcting? I dont know. I just want to know the application of it.
    – mallea
    Aug 2 at 2:25






  • 1




    I have used the concept in 7 old answers. That may be a start? Anyway, there is a section of their theory in Lidl & Niederreiter. D. Goss's book Arithmetic on Function Fields has quite a bit more, but may run a bit deep (depending on your background). I first encountered when working with character sums related to quadratic forms (or, polynomials in characteristic two such that all the exponents has binary weight two).
    – Jyrki Lahtonen
    Aug 2 at 21:45














up vote
1
down vote

favorite
1












I read the wikipedia article on Linearized polynomials.



But I'm not sure the quite use-case of it.



Can anyone elaborate on it?




field-theory finite-fields




share|cite|improve this question






















  • Can you explain better your question?
    – Taroccoesbrocco
    Aug 1 at 11:18










  • @Taroccoesbrocco what's linearized polynomial for? For example, when do we use that polynomial? Cryptography? Error Correcting? I dont know. I just want to know the application of it.
    – mallea
    Aug 2 at 2:25






  • 1




    I have used the concept in 7 old answers. That may be a start? Anyway, there is a section of their theory in Lidl & Niederreiter. D. Goss's book Arithmetic on Function Fields has quite a bit more, but may run a bit deep (depending on your background). I first encountered when working with character sums related to quadratic forms (or, polynomials in characteristic two such that all the exponents has binary weight two).
    – Jyrki Lahtonen
    Aug 2 at 21:45












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





I read the wikipedia article on Linearized polynomials.



But I'm not sure the quite use-case of it.



Can anyone elaborate on it?




field-theory finite-fields




share|cite|improve this question














I read the wikipedia article on Linearized polynomials.



But I'm not sure the quite use-case of it.



Can anyone elaborate on it?





field-theory finite-fields





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 10 at 17:45









Jyrki Lahtonen

105k12161355




105k12161355










asked Aug 1 at 11:06









mallea

29618




29618











  • Can you explain better your question?
    – Taroccoesbrocco
    Aug 1 at 11:18










  • @Taroccoesbrocco what's linearized polynomial for? For example, when do we use that polynomial? Cryptography? Error Correcting? I dont know. I just want to know the application of it.
    – mallea
    Aug 2 at 2:25






  • 1




    I have used the concept in 7 old answers. That may be a start? Anyway, there is a section of their theory in Lidl & Niederreiter. D. Goss's book Arithmetic on Function Fields has quite a bit more, but may run a bit deep (depending on your background). I first encountered when working with character sums related to quadratic forms (or, polynomials in characteristic two such that all the exponents has binary weight two).
    – Jyrki Lahtonen
    Aug 2 at 21:45
















  • Can you explain better your question?
    – Taroccoesbrocco
    Aug 1 at 11:18










  • @Taroccoesbrocco what's linearized polynomial for? For example, when do we use that polynomial? Cryptography? Error Correcting? I dont know. I just want to know the application of it.
    – mallea
    Aug 2 at 2:25






  • 1




    I have used the concept in 7 old answers. That may be a start? Anyway, there is a section of their theory in Lidl & Niederreiter. D. Goss's book Arithmetic on Function Fields has quite a bit more, but may run a bit deep (depending on your background). I first encountered when working with character sums related to quadratic forms (or, polynomials in characteristic two such that all the exponents has binary weight two).
    – Jyrki Lahtonen
    Aug 2 at 21:45















Can you explain better your question?
– Taroccoesbrocco
Aug 1 at 11:18




Can you explain better your question?
– Taroccoesbrocco
Aug 1 at 11:18












@Taroccoesbrocco what's linearized polynomial for? For example, when do we use that polynomial? Cryptography? Error Correcting? I dont know. I just want to know the application of it.
– mallea
Aug 2 at 2:25




@Taroccoesbrocco what's linearized polynomial for? For example, when do we use that polynomial? Cryptography? Error Correcting? I dont know. I just want to know the application of it.
– mallea
Aug 2 at 2:25




1




1




I have used the concept in 7 old answers. That may be a start? Anyway, there is a section of their theory in Lidl & Niederreiter. D. Goss's book Arithmetic on Function Fields has quite a bit more, but may run a bit deep (depending on your background). I first encountered when working with character sums related to quadratic forms (or, polynomials in characteristic two such that all the exponents has binary weight two).
– Jyrki Lahtonen
Aug 2 at 21:45




I have used the concept in 7 old answers. That may be a start? Anyway, there is a section of their theory in Lidl & Niederreiter. D. Goss's book Arithmetic on Function Fields has quite a bit more, but may run a bit deep (depending on your background). I first encountered when working with character sums related to quadratic forms (or, polynomials in characteristic two such that all the exponents has binary weight two).
– Jyrki Lahtonen
Aug 2 at 21:45















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