Linear block codes over cyclic groups
Copyright policy )Linear block codes over cyclic groups
The concept of geometrically uniformed (GU) code was introduced by \textit{G. D. Forney} [IEEE Trans. Inform. Theory 37, No. 5, 1241-1260 (1991; Zbl 0734.94026).] If \(I\) denotes an index set and \(C\) a subgroup of the Cartesian product group \(G^I\) then a GU code \(C\) is obtained by mapping the codewords \(c \in C\) to signal sequences \(s \in C\) according to isometric labeling \(m\) extended componentwise, i.e. \(C = m(C) = \{s \in (\mathbb{R}^N)^I : s = m(c)\), \(c\in C\}\). In this paper the authors investigate the case of \(G\) being cyclic. Besides some examples of coded modulation schemes trellis construction and bounds on the minimum Euclidean distance are also investigated.
Other types of codes, Finite automorphism groups of algebraic, geometric, or combinatorial structures, geometrically uniformed code, block codes, coded modulation schemes, trellis construction, bound, minimum Euclidean distance, Combined modulation schemes (including trellis codes) in coding theory, Linear codes (general theory)
Other types of codes, Finite automorphism groups of algebraic, geometric, or combinatorial structures, geometrically uniformed code, block codes, coded modulation schemes, trellis construction, bound, minimum Euclidean distance, Combined modulation schemes (including trellis codes) in coding theory, Linear codes (general theory)
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