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Extended linear codę

Error control capability of an (n,k) linear codę can be improved by adding an ovcrall parity-check bit. An extended codę (/? + U) is obtained. The addition of such bit incrcascs a codę minimum distancc by one. For the Hamming cxtcnded codę: d^ =4. what enablcs single-error correction and also double error detection. A codę parity-check equations are supplemcnted with an ovcrall parity-check sum:

= ś® w,

)= i

Thcn. the parity-check matrix of an extended codę can be obtained by adding at the right side. the all-0 column (original codę parity-check equations remain unchanged) and then, by adding at the bottom, the all-1 row (overall parity-check).

Decoder calculates two syndromes: original (Hamming) codę syndrome s_H and parity-check syndrome:

«♦!

^sP = X^0vy

>=«

They designate the decoder decision.