A linear block code (LBC) with a minimum distance of $d_{m i n} = 4$ ,

can detect upto 2 bit errors and simultaneously correct upto 1 bit errors.

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can detect upto 2 bit errors and simultaneously correct upto 2 bit errors.

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can detect upto 4 bit errors and simultaneously correct upto 1 bit errors.

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can detect upto 3 bit errors and simultaneously correct upto 1 bit errors.

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Solution

The correct option is A can detect upto 2 bit errors and simultaneously correct upto 1 bit errors.
The conditions to detect upto $^{'} c_{d}$ ' bit errors and simultaneously correct upto $^{'} c_{c}^{'}$ bit errors is,

$d_{m i n} \geq (c_{d} + c_{c} + 1)$

For the given LBC $= d_{m i n} = 4$

So, $c_{d} + c_{c} + 1 \leq 4$

$c_{d} + c_{c} \leq 3$
Only option (c) satisfies the above condition.

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