MinT - Information on Result #1833735

Information on Result #1833735

OOA(4²⁴⁹, 654, S₄, 2, 63), using trace code based on OOA(64⁸³, 218, S₆₄, 2, 63), using

discarding parts of the base [i] based on linear OOA(128⁷¹, 218, F₁₂₈, 2, 63) (dual of [(218, 2), 365, 64]-NRT-code), using
- constructionÂ X applied to AG(2;F,366P) âŠ‚ AG(2;F,370P) [i] based on
  1. linear OOA(128⁶⁸, 215, F₁₂₈, 2, 63) (dual of [(215, 2), 362, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,366P) [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]
  2. linear OOA(128⁶⁴, 215, F₁₂₈, 2, 59) (dual of [(215, 2), 366, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,370P) [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216 (see above)
  3. linear OOA(128³, 3, F₁₂₈, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128³, 128, F₁₂₈, 2, 3) (dual of [(128, 2), 253, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;253,128) [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(4²⁵¹, 655, S₄, 2, 63)	[i]		NRT-Code Embedding in Larger Space
2	OOA(4²⁵⁰, 654, S₄, 2, 63)	[i]		OOA Duplication