Wadayama, Tadashi; Wakasugi, Koichiro; Kasahara, Masao On weight distribution for Euclidean image of binary linear codes. (English) Zbl 0944.94013 Mem. Fac. Eng. Des., Kyoto Inst. Technol., Ser. Sci. Technol. 45, 43-54 (1996). Summary: Some properties of weight distribution for the Euclidean image of binary linear codes are investigated. Many codes defined on Euclidean space can be regarded as the image of binary linear code with a mapping (from binary to signal constellation). The authors first show the duality of weight distribution for the Euclidean image based on a binary linear code \(C\) and its dual code \(C^\perp\). In general, the weight distribution of the Euclidean image is not distance invariant. The authors present new upper and lower bounds of weight distributions. Furthermore, they present the condition of distance invariance explicitly. Finally, they discuss the computation time of the weight enumerator and an extension of upper and lower bounds for group codes. Cited in 1 Document MSC: 94B05 Linear codes (general theory) 94B65 Bounds on codes Keywords:weight distribution; Euclidean image; binary linear codes; bounds; distance invariance; group codes PDFBibTeX XMLCite \textit{T. Wadayama} et al., Mem. Fac. Eng. Des., Kyoto Inst. Technol., Ser. Sci. Technol. 45, 43--54 (1996; Zbl 0944.94013)