MinT - Information on Result #2709523

Information on Result #2709523

OOA(8¹²⁷, 581, S₈, 3, 40), using 1 times NRT-code embedding in larger space based on OOA(8¹²⁴, 580, S₈, 3, 40), using

trace code [i] based on OOA(64⁶², 290, S₆₄, 3, 40), using
- discarding parts of the base [i] based on linear OOA(128⁵³, 290, F₁₂₈, 3, 40) (dual of [(290, 3), 817, 41]-NRT-code), using
  - constructionÂ X applied to AG(3;F,820P) âŠ‚ AG(3;F,825P) [i] based on
    1. linear OOA(128⁴⁹, 287, F₁₂₈, 3, 40) (dual of [(287, 3), 812, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,820P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]
    2. linear OOA(128⁴⁴, 287, F₁₂₈, 3, 35) (dual of [(287, 3), 817, 36]-NRT-code), using algebraic-geometric NRT-code AG(3;F,825P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
    3. linear OOA(128⁴, 3, F₁₂₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(128⁴, 128, F₁₂₈, 3, 4) (dual of [(128, 3), 380, 5]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;380,128) [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(8¹²⁸, 581, S₈, 3, 40)	[i]		OOA Duplication
2	OOA(8¹²⁹, 581, S₈, 3, 40)	[i]		OOA Duplication