Pires Da Nóbrega Neto, T. [UNESP]Interlando, J. C. [UNESP]Favareto, O. M. [UNESP]Elia, M. [UNESP]Palazzo R., Jr [UNESP]2014-05-272014-05-272001-05-01IEEE Transactions on Information Theory, v. 47, n. 4, p. 1514-1527, 2001.0018-9448http://hdl.handle.net/11449/66509We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.1514-1527engAlgebraic decodingEuclidean domainsLatticesLinear codesMannheim distanceNumber fieldsSignal sets matched to groupsAlgorithmsCodes (symbols)DecodingError analysisLinearizationMaximum likelihood estimationMaximum principleNumber theoryQuadratic programmingQuadrature amplitude modulationTwo dimensionalVector quantizationEinstein-Jacobi integersGaussian integersHamming distanceLattice codesLattice constellationsManhattan metric moduloMannheim metricMaximum distance separableQuadratic number fieldsInformation theoryArtigo10.1109/18.923731WOS:000168790600017Acesso restrito2-s2.0-0035334579