MinT - Information on Result #940055

Information on Result #940055

Linear OOA(5¹³⁰, 406, F₅, 2, 36) (dual of [(406, 2), 682, 37]-NRT-code), using trace code based on linear OOA(25⁶⁵, 203, F₂₅, 2, 36) (dual of [(203, 2), 341, 37]-NRT-code), using

constructionÂ X applied to AG(2;F,361P) âŠ‚ AG(2;F,366P) [i] based on
1. linear OOA(25⁶¹, 199, F₂₅, 2, 36) (dual of [(199, 2), 337, 37]-NRT-code), using algebraic-geometric NRT-code AG(2;F,361P) [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(25⁵⁶, 199, F₂₅, 2, 31) (dual of [(199, 2), 342, 32]-NRT-code), using algebraic-geometric NRT-code AG(2;F,366P) [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200 (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(5¹³¹, 406, F₅, 2, 36) (dual of [(406, 2), 681, 37]-NRT-code)	[i]		OOA Duplication