MinT - Information on Result #1047738

Information on Result #1047738

Linear OOA(2¹⁷⁰, 116, F₂, 3, 48) (dual of [(116, 3), 178, 49]-NRT-code), using trace code based on linear OOA(4⁸⁵, 58, F₄, 3, 48) (dual of [(58, 3), 89, 49]-NRT-code), using

constructionÂ X applied to AG(3;F,116P) âŠ‚ AG(3;F,121P) [i] based on
1. linear OOA(4⁸¹, 55, F₄, 3, 48) (dual of [(55, 3), 84, 49]-NRT-code), using algebraic-geometric NRT-code AG(3;F,116P) [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(4⁷⁶, 55, F₄, 3, 43) (dual of [(55, 3), 89, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,121P) [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		This result only	Method
1	Linear OOA(2¹⁷⁰, 58, F₂, 5, 48) (dual of [(58, 5), 120, 49]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁷⁰, 58, F₂, 6, 48) (dual of [(58, 6), 178, 49]-NRT-code)	[i]		OOA Folding