MinT - Information on Result #1189102

Information on Result #1189102

Digital (72, 89, 1958)-net over F₅, using net defined by OOA based on linear OOA(5⁸⁹, 1958, F₅, 17, 17) (dual of [(1958, 17), 33197, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(5⁸⁹, 15665, F₅, 17) (dual of [15665, 15576, 18]-code), using
- constructionÂ X applied to C_e(16) âŠ‚ C_e(10) [i] based on
  1. linear OA(5⁷⁹, 15625, F₅, 17) (dual of [15625, 15546, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  2. linear OA(5⁴⁹, 15625, F₅, 11) (dual of [15625, 15576, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(5¹⁰, 40, F₅, 5) (dual of [40, 30, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹⁰, 52, F₅, 5) (dual of [52, 42, 6]-code), using
      - trace code [i] based on linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
        extended Reedâ€“Solomon code RS_e(21,25) [i]
        the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
        algebraic-geometric code AG(F, Q+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

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.