I NEED REAL HUMAN EXPERT ANSWER $,$ NOT AI UNCORRECT$/$UNCOMPLETE ANSWERS THAT I CAN FIND IN ANY AIWEBSITE FOR FREE

I PAYING FOR EXPERT ANSWER NOT AI

given linear code block with generating matrix $15,3$

G$=$

$100100100100100$

$010010010010010$

$001001001001001$

find a case of $5$ errors that the code unable to recognise and case of $12$ errors the code can recognise

also find a case the of $6$ erros the code can fix and case of $4$ errors the code unable to fix

it is question of find specific case that it can or cannot do $,$ for example burst errors cases

minimum distance is $3$ as of hamming code. so

FIXING ABILITY OF THE CODE IS $1$

as I tried:

$6$ errors case can fix:

V$=111111111100100$ in this case original data bits didnt change so the code can fix it

$4$ erros cant fix:

V$=011000100100100$ because $2$ data bits changed $($code can fix only $1)$

$12$ erros that cn recognize so syndrome is not $000$

for example

e$=111111111000111$ this will be syndrom $(1,1,1)$ so code recognising there are errors

case of $5$ that cant recognise I couldnt find because from $5$ erros cant build syndrom of $0,0,0,,$ for $0,0,0$ need all parity to be $0$ and $5$ is odd number

are my answer correct?

every answer of possible syndrom ressult, need to proof that the syndrom is really what expected $($syndrom of e $=[111110000000000]$ is not $0,0,0,)$