Note on the Characterization of Rings of Integers in View of Arithmetic Codes |
Common terms and phrases
2+1 mod a₂ Abelian group addition mod additive identity additive structure ALGEBRAIC STRUCTURE Arithmetic associated arithmetic codes arithmetic is performed binary canonical homomorphism carry-around check addition checking an addition code design code for addition code space coding theory communication codes complement computer as operations consider considerd construct the code contain all information cyclic group data space define a map detecting or correcting easily implemented encoded form equivalence class Euclidean ring Example of checking extra finite group-homomorphism ideal integers modulo isomorphism Ker 9 Ker q m₁ m₂ map elements map is well-defined module module-homomorphism n₂ negative numbers nonnegative integer nonseparate codes NSIDERATIONS Obviously Overflow conditions Proof Necess properties R-module reducing modulo Remark represent negative representation residue classes result ring multiplication ring-homomorphism scalar multiplication separate code sign bit single errors STRUCTURE OF ARITHMETIC submodule subset theorem trivial observation verify all bits Vr,s want to check weight