MinT - Information on Result #899951

Information on Result #899951

Linear OOA(25⁸⁵, 7886, F₂₅, 2, 23) (dual of [(7886, 2), 15687, 24]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁵, 66, F₂₅, 2, 11) (dual of [(66, 2), 117, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,120P) [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(25⁷⁰, 7820, F₂₅, 2, 23) (dual of [(7820, 2), 15570, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁰, 15640, F₂₅, 23) (dual of [15640, 15570, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁷⁰, 15641, F₂₅, 23) (dual of [15641, 15571, 24]-code), using
    - constructionÂ X applied to C([0,11]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(25⁶⁷, 15626, F₂₅, 23) (dual of [15626, 15559, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626Â | 25⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
      2. linear OA(25⁵⁵, 15626, F₂₅, 19) (dual of [15626, 15571, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626Â | 25⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(25³, 15, F₂₅, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-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.