منابع مشابه
Constacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملOn Skew Cyclic Codes over a Finite Ring
In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
متن کاملGray Images of Constacyclic Codes over some Polynomial Residue Rings
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 کاملCyclic Codes and Self-Dual Codes Over
We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u = 0 and study them by analogy with the Z4 case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z4-codes. Unlike the Z4 case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-d...
متن کاملConvolutional Codes Over Rings
Elementary information about convolutional codes over finite fields is introduced, and various motivations for extension to convolutional codes over finite rings are discussed. The recent primary motivation is found to be for use over phase modulation signals. Such ring codes enjoy the special property of phase weight equal to phase distance equal to the squared Euclidean distance between phase...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae - General Algebra and Applications
سال: 2017
ISSN: 1509-9415,2084-0373
DOI: 10.7151/dmgaa.1277