MinT - Information on Result #1837707

Information on Result #1837707

OOA(8¹⁴⁰, 584, S₈, 3, 44), using trace code based on OOA(64⁷⁰, 292, S₆₄, 3, 44), using

discarding parts of the base [i] based on linear OOA(128⁶⁰, 292, F₁₂₈, 3, 44) (dual of [(292, 3), 816, 45]-NRT-code), using
- constructionÂ X applied to AG(3;F,816P) âŠ‚ AG(3;F,824P) [i] based on
  1. linear OOA(128⁵³, 287, F₁₂₈, 3, 44) (dual of [(287, 3), 808, 45]-NRT-code), using algebraic-geometric NRT-code AG(3;F,816P) [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(128⁴⁵, 287, F₁₂₈, 3, 36) (dual of [(287, 3), 816, 37]-NRT-code), using algebraic-geometric NRT-code AG(3;F,824P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
  3. linear OOA(128⁷, 5, F₁₂₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁷, 128, F₁₂₈, 3, 7) (dual of [(128, 3), 377, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;377,128) [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(8¹⁴⁰, 584, S₈, 3, 43)	[i]		Strength Reduction for OOAs
2	OOA(8¹⁴³, 585, S₈, 3, 44)	[i]		NRT-Code Embedding in Larger Space
3	OOA(8¹⁴¹, 584, S₈, 3, 44)	[i]		OOA Duplication
4	OOA(8¹⁴², 584, S₈, 3, 44)	[i]		OOA Duplication