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The article is devoted to an important role of the concept of resonances not only in classical and quantum mechanics but also in genetics and biological communication. Matrix representations of oscillators with many degrees of freedom are used to model some phenomena of Mendelian genetics and to analyze structures of genetic-molecular alphabets. To explain phenomena of segregation in these molecular alphabets, the existence of dominant and recessive resonances in nitrogenous bases of DNA and RNA are postulated by analogy with dominant and recessive alleles in Mendelian genetics. Relations of genetic alphabets with modulo-2 addition, dyadic groups of binary numbers and matrices of dyadic shifts are shown. A connection of structures of genetic alphabets with known formalisms of noiseimmunity coding (Rademacher and Walsh functions, Hadamard matrices) are discussed taking into account noise-immunity properties of genetic encoding.