MinT - Information on Result #1010847

Information on Result #1010847

Linear OOA(3²⁴¹, 5592416, F₃, 3, 16) (dual of [(5592416, 3), 16777007, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁸¹, 2796209, F₃, 3, 8) (dual of [(2796209, 3), 8388546, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 8, F₃, 3, 4) (dual of [(8, 3), 19, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 5, 8)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(3⁷⁶, 2796201, F₃, 3, 8) (dual of [(2796201, 3), 8388527, 9]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(3¹⁶⁰, 2796208, F₃, 3, 16) (dual of [(2796208, 3), 8388464, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁹, 7, F₃, 3, 8) (dual of [(7, 3), 12, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3¹⁵¹, 2796201, F₃, 3, 16) (dual of [(2796201, 3), 8388452, 17]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.