MinT - Information on Result #2524643

Information on Result #2524643

OOA(4²²², 247, S₄, 2, 73), using 1 times NRT-code embedding in larger space based on OOA(4²²⁰, 246, S₄, 2, 73), using

trace code [i] based on OOA(16¹¹⁰, 123, S₁₆, 2, 73), using
- discarding parts of the base [i] based on linear OOA(32⁸⁸, 123, F₃₂, 2, 73) (dual of [(123, 2), 158, 74]-NRT-code), using
  - constructionÂ X applied to AG(2;F,164P) âŠ‚ AG(2;F,169P) [i] based on
    1. linear OOA(32⁸⁴, 119, F₃₂, 2, 73) (dual of [(119, 2), 154, 74]-NRT-code), using algebraic-geometric NRT-code AG(2;F,164P) [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(32⁷⁹, 119, F₃₂, 2, 68) (dual of [(119, 2), 159, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,169P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120 (see above)
    3. linear OOA(32⁴, 4, F₃₂, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(32⁴, 32, F₃₂, 2, 4) (dual of [(32, 2), 60, 5]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;60,32) [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(4²²³, 247, S₄, 2, 73)	[i]		OOA Duplication