MinT - Information on Result #939341

Information on Result #939341

Linear OOA(4¹⁷⁰, 170, F₄, 2, 58) (dual of [(170, 2), 170, 59]-NRT-code), using trace code based on linear OOA(16⁸⁵, 85, F₁₆, 2, 58) (dual of [(85, 2), 85, 59]-NRT-code), using

constructionÂ X applied to AG(2;F,69P) âŠ‚ AG(2;F,90P) [i] based on
1. linear OOA(16⁶⁴, 64, F₁₆, 2, 58) (dual of [(64, 2), 64, 59]-NRT-code), using algebraic-geometric NRT-code AG(2;F,69P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
2. linear OOA(16⁴³, 64, F₁₆, 2, 37) (dual of [(64, 2), 85, 38]-NRT-code), using algebraic-geometric NRT-code AG(2;F,90P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
3. linear OOA(16²¹, 21, F₁₆, 2, 20) (dual of [(21, 2), 21, 21]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16²¹, 24, F₁₆, 2, 20) (dual of [(24, 2), 27, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,27P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁷¹, 170, F₄, 2, 58) (dual of [(170, 2), 169, 59]-NRT-code)	[i]		OOA Duplication