MinT - Information on Result #900074

Information on Result #900074

Linear OOA(25⁹⁶, 7884, F₂₅, 2, 27) (dual of [(7884, 2), 15672, 28]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁷, 66, F₂₅, 2, 13) (dual of [(66, 2), 115, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,118P) [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(25⁷⁹, 7818, F₂₅, 2, 27) (dual of [(7818, 2), 15557, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁹, 15636, F₂₅, 27) (dual of [15636, 15557, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁷⁹, 15637, F₂₅, 27) (dual of [15637, 15558, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
      1. linear OA(25⁷⁶, 15625, F₂₅, 27) (dual of [15625, 15549, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(25⁶⁷, 15625, F₂₅, 23) (dual of [15625, 15558, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(25³, 12, F₂₅, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,25) or 12-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.