MinT - Information on Result #1189146

Information on Result #1189146

Digital (124, 141, 1048578)-net over F₅, using net defined by OOA based on linear OOA(5¹⁴¹, 1048578, F₅, 18, 17) (dual of [(1048578, 18), 18874263, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(5¹⁴¹, 4194313, F₅, 2, 17) (dual of [(4194313, 2), 8388485, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹⁰, 12, F₅, 2, 8) (dual of [(12, 2), 14, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,15P) [i] based on function field F/F₅ with g(F) = 2 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(5¹³¹, 4194301, F₅, 2, 17) (dual of [(4194301, 2), 8388471, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(5¹³¹, 8388602, F₅, 17) (dual of [8388602, 8388471, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(5¹³¹, large, F₅, 17) (dual of [large, large−131, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.