Codes Over Rings of Algebraic Integers
نویسندگان
چکیده
منابع مشابه
Algebraic Geometric Codes over Rings
Whenever information is transmitted across a channel, errors are likely to occur. Since Shannon’s groundbreaking paper [36], coding theorists have sought to construct codes that have many codewords, that are easy to encode and decode, and that correct errors. While the main tools used in coding theory have traditionally been those of combinatorics and group theory, this volume is dedicated to c...
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In this study, we obtain new classes of linear codes over Hurwitz integers equipped with a new metric. We refer to the metric as Hurwitz metric. The codes with respect to Hurwitz metric use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither Hamming metric nor Lee metric. Also, we define decoding algorithms for these codes when up to...
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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 کاملConvolutional Codes Over Rings
Convolutional codes over rings behave quite differently from convolutional codes over fields, but they are the ones best suited for phase modulation. This behavior depends strongly on the structure of the underlying ring. Some basic concepts about ring convolutional codes, in particular over Zpr , and their structural properties such as basicity, systematicity, non-catastrophicity and minimalit...
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: Journal of Communication and Information Systems
سال: 1998
ISSN: 1980-6604,1980-6604
DOI: 10.14209/jcis.1998.7