In the proper enumeration of the binary words, the sequence is arranged as {X1,X2,X3,X4,X5,X6,X7,X8,X9,…}:={0,1,00,01,10,11,000,001,010,…}. Simple methods for finding the index of a given word in this proper enumeration are presented and analyzed. Additionally, methods for determining the corresponding word from a given index in this enumeration are described. These methods are extended to any radix-r word system.
On the proper enumeration of all finite length strings for source coding
Tallini, Luca G.
2026-01-01
Abstract
In the proper enumeration of the binary words, the sequence is arranged as {X1,X2,X3,X4,X5,X6,X7,X8,X9,…}:={0,1,00,01,10,11,000,001,010,…}. Simple methods for finding the index of a given word in this proper enumeration are presented and analyzed. Additionally, methods for determining the corresponding word from a given index in this enumeration are described. These methods are extended to any radix-r word system.File in questo prodotto:
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