MinT - Information on Result #1837692

Information on Result #1837692

OOA(8¹²⁶, 582, S₈, 3, 39), using trace code based on OOA(64⁶³, 291, S₆₄, 3, 39), using

discarding parts of the base [i] based on linear OOA(128⁵⁴, 291, F₁₂₈, 3, 39) (dual of [(291, 3), 819, 40]-NRT-code), using
- constructionÂ X applied to AG(3;F,821P) âŠ‚ AG(3;F,828P) [i] based on
  1. linear OOA(128⁴⁸, 287, F₁₂₈, 3, 39) (dual of [(287, 3), 813, 40]-NRT-code), using algebraic-geometric NRT-code AG(3;F,821P) [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(128⁴¹, 287, F₁₂₈, 3, 32) (dual of [(287, 3), 820, 33]-NRT-code), using algebraic-geometric NRT-code AG(3;F,828P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
  3. linear OOA(128⁶, 4, F₁₂₈, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁶, 128, F₁₂₈, 3, 6) (dual of [(128, 3), 378, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;378,128) [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(8¹²⁹, 583, S₈, 3, 39)	[i]		NRT-Code Embedding in Larger Space
2	OOA(8¹²⁷, 582, S₈, 3, 39)	[i]		OOA Duplication
3	OOA(8¹²⁸, 582, S₈, 3, 39)	[i]		OOA Duplication