~

codes/classical/bits/cyclic/extended_golay.yml

@@ -45,9 +45,9 @@ relations:
       detail: 'The Golay code and several of its extended, shortened, and punctured versions are LP universally optimal codes \cite{arxiv:1212.1913}.'
   cousins:
     - code_id: icosahedron
-      detail: 'The parity bits of the extended Golay code can be visualized to lie on the vertices of the icosahedron; see \href{https://blogs.ams.org/visualinsight/2015/12/01/golay-code/}{post} by J. Baez for more details. To construct the Golay code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.'
+      detail: 'The parity bits of the extended Golay code can be visualized to lie on the vertices of the icosahedron; see \href{https://blogs.ams.org/visualinsight/2015/12/01/golay-code/}{post} by J. Baez for more details. To construct the code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.'
     - code_id: dodecahedron
-      detail: 'The parity bits of the extended Golay code can be visualized to lie on the vertices of the icosahedron; see \href{https://blogs.ams.org/visualinsight/2015/12/01/golay-code/}{post} by J. Baez for more details. To construct the Golay code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.'
+      detail: 'The parity bits of the extended Golay code can be visualized to lie on the vertices of the icosahedron; see \href{https://blogs.ams.org/visualinsight/2015/12/01/golay-code/}{post} by J. Baez for more details. To construct the code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.'
     - code_id: golay
       detail: 'The extended Golay code is an extension of the Golay code by a parity-check bit.'
 

codes/classical/properties/block/universally_optimal/t-designs.yml

@@ -32,7 +32,7 @@ description: |
   More generally, designs exist when \(X\) is \(q\)-ary Hamming space, ordered Hamming space \cite{doi:10.4153/CJM-1999-017-5,arXiv:cs/0702033}, \(q\)-Johnson space \cite{manual:{Cameron, Peter J. "Generalisation of Fisher’s inequality to fields with more than one element." Combinatorics, London Math. Soc. Lecture Note Ser 13 (1973): 9-13.},doi:10.1145/2488608.2488715} (where they are called \hyperref[code:subspace_design]{subspace designs}), a sphere \cite{doi:10.1007/BF03187604} (where they are called \hyperref[code:spherical_design]{spherical designs}), or a compact connected two-point homogeneous space \cite{doi:10.1109/18.720545,preset:HPLevBounds,arXiv:1308.3188} (the sphere or the real, complex, quaternionic, or octonionic projective spaces \cite{doi:10.2307/1969427}).
 
   Complex projective designs are designs on the space of all quantum states \cite{arXiv:quant-ph/0310075,arxiv:quant-ph/0701126,doi:10.1017/9781139207010}.
-  Symmetric informationally complete quantum measurements (SIC-POVMs) \cite{arXiv:quant-ph/0310075} and mutually unbiased bases (MUBs) \cite{arxiv:quant-ph/0309120,arxiv:quant-ph/0502031,arxiv:0711.1017,arxiv:1004.3348,arxiv:1505.01123} are important examples of such designs.
+  Symmetric informationally complete quantum measurements (SIC-POVMs) \cite{manual:{Zauner, G. (1999). Grundzüge einer nichtkommutativen Designtheorie. Ph. D. dissertation, PhD thesis.},arXiv:quant-ph/0310075} and mutually unbiased bases (MUBs) \cite{arxiv:quant-ph/0309120,arxiv:quant-ph/0502031,arxiv:0711.1017,arxiv:1004.3348,arxiv:1505.01123} are important examples of such designs.
   A limit of infinite dimensions yields rigged designs or, more colloquially, continuous-variable (CV) designs \cite{arxiv:2211.05127}, which can be used as operator-valued measures for the space of bosonic quantum states (i.e., Schwartz space over the reals).
 
   Designs also exist on groups.