MinT - Information on Result #899675

Information on Result #899675

Linear OOA(25⁷⁵, 195385, F₂₅, 2, 16) (dual of [(195385, 2), 390695, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹², 66, F₂₅, 2, 8) (dual of [(66, 2), 120, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,123P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(25⁶³, 195319, F₂₅, 2, 16) (dual of [(195319, 2), 390575, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁶³, 390638, F₂₅, 16) (dual of [390638, 390575, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁶³, 390639, F₂₅, 16) (dual of [390639, 390576, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
      1. linear OA(25⁶¹, 390625, F₂₅, 16) (dual of [390625, 390564, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(25⁴⁹, 390625, F₂₅, 13) (dual of [390625, 390576, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(25², 14, F₂₅, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,25)), using
        discarding factors / shortening the dual code based on linear OA(25², 25, F₂₅, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
        Reedâ€“Solomon code RS(23,25) [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

None.