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== Theorem | == Theorem 9 (Ternary product words) == | ||
If a [[product word]] of two MOS words of the same length is ternary, then it is pairwise-MOS. | |||
=== Proof === | === Proof === | ||
Assume that the product of two MOS words ''v''('''a''', '''b''') and ''w''('''c''', '''d''') contains exactly three letters, say ('''a''', '''c'''), ('''a''', '''d'''), ('''b''', '''c'''). Equating ('''a''', '''c''') and ('''a''', '''d''') recovers ''v'', and equating ('''a''', '''c''') and ('''b''', '''c''') recovers ''w''. What does equating ('''a''', '''d''') and ('''b''', '''c''') do? | |||