MinT - Information on Result #2524579

Information on Result #2524579

OOA(4²¹⁴, 246, S₄, 2, 70), using 2 times NRT-code embedding in larger space based on OOA(4²¹⁰, 244, S₄, 2, 70), using

trace code [i] based on OOA(16¹⁰⁵, 122, S₁₆, 2, 70), using
- discarding parts of the base [i] based on linear OOA(32⁸⁴, 122, F₃₂, 2, 70) (dual of [(122, 2), 160, 71]-NRT-code), using
  - constructionÂ X applied to AG(2;F,167P) âŠ‚ AG(2;F,171P) [i] based on
    1. linear OOA(32⁸¹, 119, F₃₂, 2, 70) (dual of [(119, 2), 157, 71]-NRT-code), using algebraic-geometric NRT-code AG(2;F,167P) [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(32⁷⁷, 119, F₃₂, 2, 66) (dual of [(119, 2), 161, 67]-NRT-code), using algebraic-geometric NRT-code AG(2;F,171P) [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(4²¹⁵, 246, S₄, 2, 70)	[i]		OOA Duplication