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Consider an $ [\![n,k]\!] $ non-stabilizer code. The weight enumerator coefficients are $$ A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2 $$ where $ \Pi $ is the projector onto the code subspace.

Are the $ A_j $ always integers?

For stabilizer codes this is true see Are the coefficients of the weight enumerator polynomial of a stabilizer code always integers?

Is it the case that the $ A_j $ are always integers for non-stabilizer codes as well? If not, what is an example of a non-stabilizer code with $ A_j $ not integers?

Consider an $ ((n,K=2^k,d)) $ non-stabilizer code. The weight enumerator coefficients are $$ A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2 $$ where $ \Pi $ is the projector onto the code subspace.

Are the $ A_j $ always integers?

For stabilizer codes this is true see Are the coefficients of the weight enumerator polynomial of a stabilizer code always integers?

Is it the case that the $ A_j $ are always integers for non-stabilizer codes as well? If not, what is an example of a non-stabilizer code with $ A_j $ not integers?

Consider an $ [\![n,k]\!] $ non-stabilizer code. The weight enumerator coefficients are $$ A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2. $$ Here $ \Pi $ is the projector onto the code subspace.

Are the $ A_j $ always integers?

For stabilizer codes this is true see Are the coefficients of the weight enumerator polynomial of a stabilizer code always integers? .

Is it the case that the $ A_j $ are always integers for non stabilizer codes as well? If not, what is an example of a non-stabilizer code with $ A_j $ not integers?

Consider an $ [\![n,k]\!] $ non-stabilizer code. The weight enumerator coefficients are $$ A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2 $$ where $ \Pi $ is the projector onto the code subspace.

Are the $ A_j $ always integers?

For stabilizer codes this is true see Are the coefficients of the weight enumerator polynomial of a stabilizer code always integers?

Is it the case that the $ A_j $ are always integers for non-stabilizer codes as well? If not, what is an example of a non-stabilizer code with $ A_j $ not integers?

Consider an $ [\![n,k]\!] $ non-stabilizer code. Define the weight enumerator polynomial $ A(x) $ of the code as $$ A(x):=A_0+A_1x+\dots+A_nx^n $$
where $$ A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2. $$ Here $ \Pi $ is the projector onto the code subspace. For stabilizer codes the $ A_j $ are always integers see Are the coefficients of the weight enumerator polynomial of a stabilizer code always integers? . Is it the case that the $ A_j $ are always integers for non stabilizer codes as well?

  If not, what is an example of a non-stabilizer code with $ A_j $ not integers?

Consider an $ [\![n,k]\!] $ non-stabilizer code. The weight enumerator coefficients are $$ A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2. $$ Here $ \Pi $ is the projector onto the code subspace.

Are the $ A_j $ always integers?

For stabilizer codes this is true see Are the coefficients of the weight enumerator polynomial of a stabilizer code always integers? . 

Is it the case that the $ A_j $ are always integers for non stabilizer codes as well? If not, what is an example of a non-stabilizer code with $ A_j $ not integers?