MinT - Information on Result #900138

Information on Result #900138

Linear OOA(25⁷⁸, 383, F₂₅, 2, 30) (dual of [(383, 2), 688, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁹, 66, F₂₅, 2, 15) (dual of [(66, 2), 113, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,116P) [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(25⁵⁹, 317, F₂₅, 2, 30) (dual of [(317, 2), 575, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁵⁹, 634, F₂₅, 30) (dual of [634, 575, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁵⁹, 635, F₂₅, 30) (dual of [635, 576, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(25) [i] based on
      1. linear OA(25⁵⁶, 625, F₂₅, 30) (dual of [625, 569, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(25⁴⁹, 625, F₂₅, 26) (dual of [625, 576, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(25³, 10, F₂₅, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,25) or 10-cap in PG(2,25)), using
        discarding factors / shortening the dual code based on linear OA(25³, 25, F₂₅, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
        Reedâ€“Solomon code RS(22,25) [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.