MinT - Information on Result #899873

Information on Result #899873

Linear OOA(25⁵⁸, 384, F₂₅, 2, 21) (dual of [(384, 2), 710, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁴, 66, F₂₅, 2, 10) (dual of [(66, 2), 118, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,121P) [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(25⁴⁴, 318, F₂₅, 2, 21) (dual of [(318, 2), 592, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁴⁴, 636, F₂₅, 21) (dual of [636, 592, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁴⁴, 637, F₂₅, 21) (dual of [637, 593, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(25⁴¹, 626, F₂₅, 21) (dual of [626, 585, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 626Â | 25⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(25³³, 626, F₂₅, 17) (dual of [626, 593, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 626Â | 25⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(25³, 11, F₂₅, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-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.