Coding theory MOC

Divisible code

A 𝑞-ary linear code C ≤𝕂𝑛𝑞 is 𝑚-divisible iff all codewords have Hamming weight divisible by 𝑚, #m/def/code i.e. wt⁡⃗𝐜 ∈𝑚ℤ for all ⃗𝐜 ∈C. In particular,

• a 2-divisible code is called an even code;
• a 4-divisible code is called a doubly-even code.

Properties

• An even binary linear code is a linear subcode of the even binary code.

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