MinT - Information on Result #2620665

Information on Result #2620665

Linear OOA(3⁶³, large, F₃, 3, 3), using strength reduction based on linear OOA(3⁶³, large, F₃, 3, 5), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁵, 7174453, F₃, 3, 2) (dual of [(7174453, 3), 21523344, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(3¹⁵, 7174453, F₃, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(3¹⁵, 7174453, F₃, 2) (dual of [7174453, 7174438, 3]-code), using
      - Hamming code H(15,3) [i]
2. linear OOA(3⁴⁸, 4194305, F₃, 3, 5) (dual of [(4194305, 3), 12582867, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3², 4, F₃, 3, 2) (dual of [(4, 3), 10, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;10,3) [i]
    2. linear OOA(3⁴⁶, 4194301, F₃, 3, 5) (dual of [(4194301, 3), 12582857, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.