MinT - Information on Result #1196716

Information on Result #1196716

Digital (55, 75, 1577)-net over F₂₅, using net defined by OOA based on linear OOA(25⁷⁵, 1577, F₂₅, 22, 20) (dual of [(1577, 22), 34619, 21]-NRT-code), using

OOA 5-folding and stacking with additional row [i] based on linear OOA(25⁷⁵, 7886, F₂₅, 2, 20) (dual of [(7886, 2), 15697, 21]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(25⁶¹, 7820, F₂₅, 2, 20) (dual of [(7820, 2), 15579, 21]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁶¹, 15640, F₂₅, 20) (dual of [15640, 15579, 21]-code), using
      - constructionÂ X applied to C_e(19) âŠ‚ C_e(15) [i] based on
        linear OA(25⁵⁸, 15625, F₂₅, 20) (dual of [15625, 15567, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
        linear OA(25⁴⁶, 15625, F₂₅, 16) (dual of [15625, 15579, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.