MinT - Information on Result #939196

Information on Result #939196

Linear OOA(4¹⁵⁴, 166, F₄, 2, 52) (dual of [(166, 2), 178, 53]-NRT-code), using trace code based on linear OOA(16⁷⁷, 83, F₁₆, 2, 52) (dual of [(83, 2), 89, 53]-NRT-code), using

constructionÂ X applied to AG(2;F,75P) âŠ‚ AG(2;F,94P) [i] based on
1. linear OOA(16⁵⁸, 64, F₁₆, 2, 52) (dual of [(64, 2), 70, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,75P) [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(16³⁹, 64, F₁₆, 2, 33) (dual of [(64, 2), 89, 34]-NRT-code), using algebraic-geometric NRT-code AG(2;F,94P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
3. linear OOA(16¹⁹, 19, F₁₆, 2, 18) (dual of [(19, 2), 19, 19]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16¹⁹, 24, F₁₆, 2, 18) (dual of [(24, 2), 29, 19]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,29P) [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(4¹⁵⁵, 166, F₄, 2, 52) (dual of [(166, 2), 177, 53]-NRT-code)	[i]		OOA Duplication