diff --git a/codes/classical/bits/reed_muller/biorthogonal.yml b/codes/classical/bits/reed_muller/biorthogonal.yml index b1ce4cf36..a5b1a046d 100644 --- a/codes/classical/bits/reed_muller/biorthogonal.yml +++ b/codes/classical/bits/reed_muller/biorthogonal.yml @@ -42,8 +42,6 @@ relations: - code_id: biorthogonal_spherical detail: 'Each first-order RM code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{manual:{Forney, G. D. (2003). 6.451 Principles of Digital Communication II, Spring 2003.}}\cite[pg. 19]{preset:EricZin}. In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.' - - code_id: dual_polytope - detail: 'Orthoplexes and hypercubes are dual to each other.' # Begin Entry Meta Information diff --git a/codes/classical/spherical/polytope/infinite/biorthogonal_spherical.yml b/codes/classical/spherical/polytope/infinite/biorthogonal_spherical.yml index 48a3b9e3e..7a810b6b6 100644 --- a/codes/classical/spherical/polytope/infinite/biorthogonal_spherical.yml +++ b/codes/classical/spherical/polytope/infinite/biorthogonal_spherical.yml @@ -46,6 +46,8 @@ relations: detail: 'Biorthogonal spherical codewords form the minimal shell of the \(\mathbb{Z}^n\) hypercubic lattice.' - code_id: binary_antipodal detail: 'Each first-order RM\((1,m)\) code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{manual:{Forney, G. D. (2003). 6.451 Principles of Digital Communication II, Spring 2003.}}\cite[pg. 19]{preset:EricZin}. In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.' + - code_id: dual_polytope + detail: 'Orthoplexes and hypercubes are dual to each other.' # Begin Entry Meta Information