MinT - Information on Result #939987

Information on Result #939987

Linear OOA(5¹¹⁴, 138, F₅, 2, 49) (dual of [(138, 2), 162, 50]-NRT-code), using trace code based on linear OOA(25⁵⁷, 69, F₂₅, 2, 49) (dual of [(69, 2), 81, 50]-NRT-code), using

constructionÂ X applied to AG(2;F,80P) âŠ‚ AG(2;F,85P) [i] based on
1. linear OOA(25⁵³, 65, F₂₅, 2, 49) (dual of [(65, 2), 77, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,80P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(25⁴⁸, 65, F₂₅, 2, 44) (dual of [(65, 2), 82, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,85P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
3. linear OOA(25⁴, 4, F₂₅, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(25⁴, 25, F₂₅, 2, 4) (dual of [(25, 2), 46, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;46,25) [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(5¹¹⁵, 138, F₅, 2, 49) (dual of [(138, 2), 161, 50]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(5¹¹⁴, 69, F₅, 3, 49) (dual of [(69, 3), 93, 50]-NRT-code)	[i]		OOA Folding