Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields
We identify Narain conformal field theories (CFTs) that correspond to code lattices for quantum error-correcting codes (QECC) over integers of cyclotomic fields Q(ζp) (ζp=e2πip) for general prime p≥3. This code-lattice construction is a generalization of more familiar ones such as Construction AC fo...
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Elsevier
2025-03-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269325000681 |
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| author | Shun'ya Mizoguchi Takumi Oikawa |
| author_facet | Shun'ya Mizoguchi Takumi Oikawa |
| author_sort | Shun'ya Mizoguchi |
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| description | We identify Narain conformal field theories (CFTs) that correspond to code lattices for quantum error-correcting codes (QECC) over integers of cyclotomic fields Q(ζp) (ζp=e2πip) for general prime p≥3. This code-lattice construction is a generalization of more familiar ones such as Construction AC for ternary codes and (after the generalization stated below) Construction A for binary codes, containing them as special cases. This code-lattice construction is redescribed in terms of root and weight lattices of Lie algebras, which allows to construct lattices for codes over rings Zq with non-prime q. Corresponding Narain CFTs are found for codes embedded into quotient rings of root and weight lattices of ADE series, except E8 and Dk with k even. In a sense, this provides a unified description of the relationship between various QECCs over Fp (or Zq) and Narain CFTs. A further extension on constructing the E8 lattice from codes over the Mordell-Weil groups of extremal rational elliptic surfaces is also briefly discussed. |
| format | Article |
| id | doaj-art-7384d830946b4014b4a5cc30126c0174 |
| institution | Kabale University |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
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| series | Physics Letters B |
| spelling | doaj-art-7384d830946b4014b4a5cc30126c01742025-02-12T05:30:28ZengElsevierPhysics Letters B0370-26932025-03-01862139308Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fieldsShun'ya Mizoguchi0Takumi Oikawa1Theory Center, Institute of Particle and Nuclear Studies, KEK, Tsukuba, Ibaraki, 305-0801, Japan; SOKENDAI (The Graduate University for Advanced Studies), Tsukuba, Ibaraki, 305-0801, Japan; Corresponding author.SOKENDAI (The Graduate University for Advanced Studies), Tsukuba, Ibaraki, 305-0801, JapanWe identify Narain conformal field theories (CFTs) that correspond to code lattices for quantum error-correcting codes (QECC) over integers of cyclotomic fields Q(ζp) (ζp=e2πip) for general prime p≥3. This code-lattice construction is a generalization of more familiar ones such as Construction AC for ternary codes and (after the generalization stated below) Construction A for binary codes, containing them as special cases. This code-lattice construction is redescribed in terms of root and weight lattices of Lie algebras, which allows to construct lattices for codes over rings Zq with non-prime q. Corresponding Narain CFTs are found for codes embedded into quotient rings of root and weight lattices of ADE series, except E8 and Dk with k even. In a sense, this provides a unified description of the relationship between various QECCs over Fp (or Zq) and Narain CFTs. A further extension on constructing the E8 lattice from codes over the Mordell-Weil groups of extremal rational elliptic surfaces is also briefly discussed.http://www.sciencedirect.com/science/article/pii/S0370269325000681 |
| spellingShingle | Shun'ya Mizoguchi Takumi Oikawa Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields Physics Letters B |
| title | Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields |
| title_full | Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields |
| title_fullStr | Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields |
| title_full_unstemmed | Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields |
| title_short | Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields |
| title_sort | unifying error correcting code narain cft correspondences via lattices over integers of cyclotomic fields |
| url | http://www.sciencedirect.com/science/article/pii/S0370269325000681 |
| work_keys_str_mv | AT shunyamizoguchi unifyingerrorcorrectingcodenaraincftcorrespondencesvialatticesoverintegersofcyclotomicfields AT takumioikawa unifyingerrorcorrectingcodenaraincftcorrespondencesvialatticesoverintegersofcyclotomicfields |