MinT - Information on Result #939845

Information on Result #939845

Linear OOA(5⁵⁸, 138, F₅, 2, 21) (dual of [(138, 2), 218, 22]-NRT-code), using trace code based on linear OOA(25²⁹, 69, F₂₅, 2, 21) (dual of [(69, 2), 109, 22]-NRT-code), using

constructionÂ X applied to AG(2;F,108P) âŠ‚ AG(2;F,113P) [i] based on
1. linear OOA(25²⁵, 65, F₂₅, 2, 21) (dual of [(65, 2), 105, 22]-NRT-code), using algebraic-geometric NRT-code AG(2;F,108P) [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(25²⁰, 65, F₂₅, 2, 16) (dual of [(65, 2), 110, 17]-NRT-code), using algebraic-geometric NRT-code AG(2;F,113P) [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(5⁵⁹, 138, F₅, 2, 21) (dual of [(138, 2), 217, 22]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(5⁵⁸, 69, F₅, 3, 21) (dual of [(69, 3), 149, 22]-NRT-code)	[i]		OOA Folding