MinT - Information on Result #1833696

Information on Result #1833696

OOA(4¹⁸⁰, 244, S₄, 2, 58), using trace code based on OOA(16⁹⁰, 122, S₁₆, 2, 58), using

discarding parts of the base [i] based on linear OOA(32⁷², 122, F₃₂, 2, 58) (dual of [(122, 2), 172, 59]-NRT-code), using
- constructionÂ X applied to AG(2;F,179P) âŠ‚ AG(2;F,183P) [i] based on
  1. linear OOA(32⁶⁹, 119, F₃₂, 2, 58) (dual of [(119, 2), 169, 59]-NRT-code), using algebraic-geometric NRT-code AG(2;F,179P) [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(32⁶⁵, 119, F₃₂, 2, 54) (dual of [(119, 2), 173, 55]-NRT-code), using algebraic-geometric NRT-code AG(2;F,183P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120 (see above)
  3. linear OOA(32³, 3, F₃₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(32³, 32, F₃₂, 2, 3) (dual of [(32, 2), 61, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;61,32) [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(4¹⁸², 245, S₄, 2, 58)	[i]		NRT-Code Embedding in Larger Space
2	OOA(4¹⁸¹, 244, S₄, 2, 58)	[i]		OOA Duplication