MinT - Information on Result #1047772

Information on Result #1047772

Linear OOA(2²⁰⁶, 116, F₂, 3, 66) (dual of [(116, 3), 142, 67]-NRT-code), using trace code based on linear OOA(4¹⁰³, 58, F₄, 3, 66) (dual of [(58, 3), 71, 67]-NRT-code), using

constructionÂ X applied to AG(3;F,98P) âŠ‚ AG(3;F,103P) [i] based on
1. linear OOA(4⁹⁹, 55, F₄, 3, 66) (dual of [(55, 3), 66, 67]-NRT-code), using algebraic-geometric NRT-code AG(3;F,98P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4⁹⁴, 55, F₄, 3, 61) (dual of [(55, 3), 71, 62]-NRT-code), using algebraic-geometric NRT-code AG(3;F,103P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;8,4) [i]

Mode: Constructive and linear.

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		Method
1	Linear OOA(2²⁰⁶, 116, F₂, 3, 65) (dual of [(116, 3), 142, 66]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁸, 116, F₂, 3, 66) (dual of [(116, 3), 140, 67]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁶, 58, F₂, 5, 66) (dual of [(58, 5), 84, 67]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2²⁰⁶, 58, F₂, 6, 66) (dual of [(58, 6), 142, 67]-NRT-code)	[i]	OOA Folding