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National Repository of Grey Literature 1 records found  Search took 0.02 seconds. 
Codes, rings and modules
 Horáček, Jan ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
This work is focused on linear error-correcting codes over chain rings. By a linear code over a chain ring R of length n, we mean a R-submodule of the module Rn . The basic introduction to the theory of finite commutative chain rings and linear codes over them is given. We especially emphasize here their al- gebraic description. Minimal homogenous and Hamming distances of these codes are extensively studied. We explain, how the generalized Gray map can transform linear codes over a chain ring into general non-linear codes over a field. We deal with the construction of linear codes over a chain ring and the construction of generator matrices based on random generation is described. Obtained codes are compared with known results.
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