MinT - Information on Result #1833710

Information on Result #1833710

OOA(4²¹⁰, 246, S₄, 2, 69), using trace code based on OOA(16¹⁰⁵, 123, S₁₆, 2, 69), using

discarding parts of the base [i] based on linear OOA(32⁸⁴, 123, F₃₂, 2, 69) (dual of [(123, 2), 162, 70]-NRT-code), using
- constructionÂ X applied to AG(2;F,168P) âŠ‚ AG(2;F,173P) [i] based on
  1. linear OOA(32⁸⁰, 119, F₃₂, 2, 69) (dual of [(119, 2), 158, 70]-NRT-code), using algebraic-geometric NRT-code AG(2;F,168P) [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(32⁷⁵, 119, F₃₂, 2, 64) (dual of [(119, 2), 163, 65]-NRT-code), using algebraic-geometric NRT-code AG(2;F,173P) [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(4²¹², 247, S₄, 2, 69)	[i]		NRT-Code Embedding in Larger Space
2	OOA(4²¹⁴, 248, S₄, 2, 69)	[i]		NRT-Code Embedding in Larger Space
3	OOA(4²¹¹, 246, S₄, 2, 69)	[i]		OOA Duplication