MinT - Information on Result #900041

Information on Result #900041

Linear OOA(25⁷⁰, 384, F₂₅, 2, 26) (dual of [(384, 2), 698, 27]-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(25⁵³, 318, F₂₅, 2, 26) (dual of [(318, 2), 583, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁵³, 636, F₂₅, 26) (dual of [636, 583, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁵³, 637, F₂₅, 26) (dual of [637, 584, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(20) [i] based on
      1. 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]
      2. linear OA(25⁴¹, 625, F₂₅, 21) (dual of [625, 584, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(25⁴, 12, F₂₅, 4) (dual of [12, 8, 5]-code or 12-arc in PG(3,25)), using
        discarding factors / shortening the dual code based on linear OA(25⁴, 25, F₂₅, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
        Reedâ€“Solomon code RS(21,25) [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.