Python, 62 47 46 bytes

thanks to @Unrelated String for the idea of alternative input format

-1 byte thanks to @dingledooper

f=lambda p,n:0in(0in p[i::n]for i in range(n))

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C (GCC), 118 bytes

d,i,j,n,l,c;main(c,v)char**v;{for(n=atoi(v[2]);i<n;++i){c=1;for(j=i;j<strlen(v[1]);j+=n)c&=v[1][j]-48;d|=c;}return d;}

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Haskell, 50 48 bytes

-2 bytes thanks to @Unrelated String

p#n=any(\i->all(p!!)[i,i+n..length p-1])[0..n-1]

Try it online!

All the solutions do basically the same thing.

Python, 62 47 46 bytes

thanks to @Unrelated String for the idea of alternative input format

-1 byte thanks to @dingledooper

f=lambda p,n:0in(0in p[i::n]for i in range(n))

Attempt This Online!

C (gcc), 118 110 bytes

-8 bytes thanks to @ceilingcat

d,i,j,n,l,c;main(c,v)char**v;{for(n=atoi(v++[2]);c=i<n;d+=c)for(j=i++;j<strlen(*v);j+=n)c&=j[*v]-48;return d;} 

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Haskell, 50 48 bytes

-2 bytes thanks to @Unrelated String

p#n=any(\i->all(p!!)[i,i+n..length p-1])[0..n-1]

Try it online!

All the solutions do basically the same thing.

Python, 62 47 46 bytes

thanks to @Unrelated String for the idea of alternative input format

-1 byte thanks to @dingledooper

f=lambda p,n:0in(0in p[i::n]for i in range(n))

Attempt This Online!

C (GCC), 118 bytes

d,i,j,n,l,c;main(c,v)char**v;{for(n=atoi(v[2]);i<n;++i){c=1;for(j=i;j<strlen(v[1]);j+=n)c&=v[1][j]-48;d|=c;}return d;}

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Haskell, 50 bytes

f p n=any(\i->all(p!!)[i,i+n..length p-1])[0..n-1]

All the solutions do basically the same thing.

Python, 62 47 46 bytes

thanks to @Unrelated String for the idea of alternative input format

-1 byte thanks to @dingledooper

f=lambda p,n:0in(0in p[i::n]for i in range(n))

Attempt This Online!

C (GCC), 118 bytes

d,i,j,n,l,c;main(c,v)char**v;{for(n=atoi(v[2]);i<n;++i){c=1;for(j=i;j<strlen(v[1]);j+=n)c&=v[1][j]-48;d|=c;}return d;}

Attempt This Online!

Haskell, 50 48 bytes

-2 bytes thanks to @Unrelated String

p#n=any(\i->all(p!!)[i,i+n..length p-1])[0..n-1]

Try it online!

All the solutions do basically the same thing.

Python, 62 47 46 bytes

thanks to @Unrelated String for the idea of alternative input format

-1 byte thanks to @dingledooper

f=lambda p,n:0in(0in p[i::n]for i in range(n))

Attempt This Online!

C (GCC), 118 bytes

d,i,j,n,l,c;main(c,v)char**v;{for(n=atoi(v[2]);i<n;++i){c=1;for(j=i;j<strlen(v[1]);j+=n)c&=v[1][j]-48;d|=c;}return d;}

Attempt This Online!

All the solutions do basically the same thing.

Python, 62 47 46 bytes

thanks to @Unrelated String for the idea of alternative input format

-1 byte thanks to @dingledooper

f=lambda p,n:0in(0in p[i::n]for i in range(n))

Attempt This Online!

C (GCC), 118 bytes

d,i,j,n,l,c;main(c,v)char**v;{for(n=atoi(v[2]);i<n;++i){c=1;for(j=i;j<strlen(v[1]);j+=n)c&=v[1][j]-48;d|=c;}return d;}

Attempt This Online!

Haskell, 50 bytes

f p n=any(\i->all(p!!)[i,i+n..length p-1])[0..n-1]

All the solutions do basically the same thing.