In applied mathematics, the Johnson bound (named after Selmer Martin Johnson) is a limit on the size of error-correcting codes, as used in coding theory for data transmission or communications.

Definition

be a q-ary code, i.e.

is the Hamming distance.

be the set of all q nonzero entries.

:

:

):

,

,

):

(i)

(ii). Then,

is the floor function.

Remark:.

See also

• Elias Bassalygo bound

• Gilbert–Varshamov bound

• Griesmer bound

• Hamming bound

• Plotkin bound

• Singleton bound

References