Codes over finite quotients of polynomial rings
نویسندگان
چکیده
Codes over finite quotient of polynomial rings
منابع مشابه
Dual of codes over finite quotients of polynomial rings
Let A = F[x] 〈f(x)〉 , where f(x) is a monic polynomial over a finite field F. In this paper, we study the relation between A-codes and their duals. In particular, we state a counterexample and a correction to a theorem of Berger and El Amrani (Codes over finite quotients of polynomial rings, Finite Fields Appl. 25 (2014), 165–181) and present an efficient algorithm to find a system of generator...
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We consider codes defined over an affine algebra A = R[X1, . . . , Xr]/ 〈t1(X1), . . . , tr(Xr)〉, where ti(Xi) is a monic univariate polynomial over a finite commutative chain ring R. Namely, we study the A−submodules of A (l ∈ N). These codes generalize both the codes over finite quotients of polynomial rings and the multivariable codes over finite chain rings. Some codes over Frobenius local ...
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Let be the quotient ring where is the finite field of size and is a positive integer. A Gray map of length over is a special map from to ( . The Gray map is said to be a ( )-Gray map if the image of any -constacyclic code over is a -constacyclic code over the field . In this paper we investigate the existence of ( )-Gray maps over . In this direction, we find an equivalent ...
متن کامل(θ, Δ)-codes with Skew Polynomial Rings
In this paper we generalize coding theory of cyclic codes over finite fields to skew polynomial rings over finite rings. Codes that are principal ideals in quotient rings of skew polynomial rings by two sided ideals are studied. Next we consider skew codes of endomorphism type and derivation type. And we give some examples.
متن کاملMathematical Aspects of (θ, δ)-Codes with Skew Polynomial Rings
In this paper we generalize coding theory of cyclic codes over finite fields to skew polynomial rings over finite rings. Codes that are principal ideals in quotient rings of skew polynomial rings by two sided ideals are studied. Next we consider skew codes of endomorphism type and derivation type. And we give some examples. Mathematics Subject Classification: Primary 94B60; Secondary 94B15, 16D25
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عنوان ژورنال:
- Finite Fields and Their Applications
دوره 25 شماره
صفحات -
تاریخ انتشار 2014