Code

Quasi-perfect code

A 𝑞-ary code C ⊆𝑆𝑛𝑞 of length 𝑛 in alphabet 𝑆𝑞 is said to be a quasi-perfect 𝑒-correcting code (cf. Perfect code), or briefly a quasi-perfect code, iff #m/def/code

• 𝑒 =⌊𝑑−12⌋ where 𝑑 is the minimum distance of C; and
• the covering radius of C is 𝑒 +1.

Properties

• The extended code of a linear perfect code is quasi-perfect.

#state/tidy | #lang/en | #SemBr