MinT - Information on Result #940040

Information on Result #940040

Linear OOA(5¹²⁶, 258, F₅, 2, 49) (dual of [(258, 2), 390, 50]-NRT-code), using trace code based on linear OOA(25⁶³, 129, F₂₅, 2, 49) (dual of [(129, 2), 195, 50]-NRT-code), using

constructionÂ X applied to AG(2;F,200P) âŠ‚ AG(2;F,205P) [i] based on
1. linear OOA(25⁵⁹, 125, F₂₅, 2, 49) (dual of [(125, 2), 191, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,200P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
  - the Hermitian function field over F₂₅ [i]
2. linear OOA(25⁵⁴, 125, F₂₅, 2, 44) (dual of [(125, 2), 196, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,205P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (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(5¹²⁷, 258, F₅, 2, 49) (dual of [(258, 2), 389, 50]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(5¹²⁶, 129, F₅, 3, 49) (dual of [(129, 3), 261, 50]-NRT-code)	[i]		OOA Folding