MinT - Information on Result #1060711

Information on Result #1060711

Linear OOA(3²⁰⁹, 2097155, F₃, 4, 20) (dual of [(2097155, 4), 8388411, 21]-NRT-code), using OOA 2-folding based on linear OOA(3²⁰⁹, 4194310, F₃, 2, 20) (dual of [(4194310, 2), 8388411, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁰⁹, 4194311, F₃, 2, 20) (dual of [(4194311, 2), 8388413, 21]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹³, 10, F₃, 2, 10) (dual of [(10, 2), 7, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3¹⁹⁶, 4194301, F₃, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁹⁶, 8388602, F₃, 20) (dual of [8388602, 8388406, 21]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, large, F₃, 20) (dual of [large, large−196, 21]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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.

Other Results with Identical Parameters

None.

Depending Results

None.