Fano condition

Fano condition (in English Fano condition , in honor of Robert Fano ) - in coding theory - a sufficient condition for constructing a self-terminating code (in another terminology, a prefix code ). The usual formulation of this condition is as follows:

No code word can be the beginning of another code word.

More “mathematical” wording:

If the code includes the word a , then for any non-empty string b the word ab does not exist in the code.

An example of a code satisfying the Fano condition is telephone numbers in traditional telephony. If there is a number 101 in the network, the number 1012345 cannot be issued: when dialing three digits, the PBX stops understanding further dialing and connects to the addressee at 101. However, for dialing from a cellular phone, this rule no longer works because an explicit termination is required characters with the corresponding button (usually with the image of a green tube), while 101, 1010 and 1012345 can be simultaneously understood as different recipients.

The term “Fano condition” is not traditional for the Russian-speaking community.