Codes over integer residue rings
نویسندگان
چکیده
منابع مشابه
Structured LDPC Codes over Integer Residue Rings
This paper presents a new class of low-density parity-check (LDPC) codes over Z2a represented by regular, structured Tanner graphs. These graphs are constructed using Latin squares defined over a multiplicative group of a Galois ring, rather than a finite field. Our approach yields codes for a wide range of code rates and more importantly, codes whose minimum pseudocodeword weights equal their ...
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 کاملCodes over Gaussian integer rings
This work presents block codes over Gaussian integer rings. Rings of Gaussian integers extend the number of possible QAM signal constellations over Gaussian integer fields. Many well-known code constructions can be used for codes over Gaussian integer rings, e.g., the Plotkin construction or product codes. These codes enable low complexity soft decoding in the complex domain.
متن کاملMinimum Homogeneous Weights of a Class of Cyclic Codes over Primary Integer Residue Rings∗
EXTENDED ABSTRACT. Most of the results in traditional finite-field linear coding theory regarding the minimum distance of linear codes refer to the Hamming metric. Important early exceptions are given by Berlekamp’s nega-cyclic codes (cf. [1]) and Mazur’s [9] low-rate codes, both having interesting properties in terms of the Leemetric. At the beginning of the nineties of the previous century an...
متن کاملLDPC Convolutional Codes Based on Permutation Polynomials over Integer Rings
A novel algebraic construction technique for LDPC convolutional codes (LDPCCCs) based on permutation polynomials over integer rings is presented. The underlying elements of this construction technique are graph automorphisms and quasi-cyclic (QC) codes. The algebraic structure of the obtained LDPCCCs, their encoding and decoding are discussed. These new codes have a special structure, which is ...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1975
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(75)80001-5