MinT - Information on Result #1833722

Information on Result #1833722

OOA(4²²⁶, 246, S₄, 2, 75), using trace code based on OOA(16¹¹³, 123, S₁₆, 2, 75), using

discarding parts of the base [i] based on linear OOA(32⁹⁰, 123, F₃₂, 2, 75) (dual of [(123, 2), 156, 76]-NRT-code), using
- constructionÂ X applied to AG(2;F,162P) âŠ‚ AG(2;F,167P) [i] based on
  1. linear OOA(32⁸⁶, 119, F₃₂, 2, 75) (dual of [(119, 2), 152, 76]-NRT-code), using algebraic-geometric NRT-code AG(2;F,162P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]
  2. linear OOA(32⁸¹, 119, F₃₂, 2, 70) (dual of [(119, 2), 157, 71]-NRT-code), using algebraic-geometric NRT-code AG(2;F,167P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120 (see above)
  3. linear OOA(32⁴, 4, F₃₂, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(32⁴, 32, F₃₂, 2, 4) (dual of [(32, 2), 60, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;60,32) [i]

Mode: Constructive.

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	OOA(4²²⁷, 246, S₄, 2, 75)	[i]		OOA Duplication