ECC dictionary N

nearest neighbor decoding algorithm: The nearest neighbor decoding algorithm:

Input: A "received vector" v in Fⁿ .

Output: A codeword c in C closest to v.

• Enumerate the elements of the ball of (Hamming) radius t about v, denoted B_t(v), where v is the received word. Set c="fail''.
• For each w in B_t(v), check if w in C. If so, put c = w and break to the next step; otherwise ,discard w and move to the next element.
• Return c.
  

Note: "fail'' is not returned unless t> (d-1)/2.. We say that a linear C is t-error correcting if  there is at most one codeword in B_t(w), for each w in Fⁿ.