MinT - Information on Result #939364

Information on Result #939364

Linear OOA(4¹⁷², 164, F₄, 2, 62) (dual of [(164, 2), 156, 63]-NRT-code), using trace code based on linear OOA(16⁸⁶, 82, F₁₆, 2, 62) (dual of [(82, 2), 78, 63]-NRT-code), using

constructionÂ X applied to AG(2;F,65P) âŠ‚ AG(2;F,83P) [i] based on
1. linear OOA(16⁶⁸, 64, F₁₆, 2, 62) (dual of [(64, 2), 60, 63]-NRT-code), using algebraic-geometric NRT-code AG(2;F,65P) [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(16⁵⁰, 64, F₁₆, 2, 44) (dual of [(64, 2), 78, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,83P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
3. linear OOA(16¹⁸, 18, F₁₆, 2, 17) (dual of [(18, 2), 18, 18]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16¹⁸, 24, F₁₆, 2, 17) (dual of [(24, 2), 30, 18]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,30P) [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(4¹⁷³, 164, F₄, 2, 62) (dual of [(164, 2), 155, 63]-NRT-code)	[i]		OOA Duplication