MinT - Information on Result #1117784

Information on Result #1117784

Linear OOA(3²³⁹, 1682648, F₃, 5, 18) (dual of [(1682648, 5), 8413001, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵⁹, 4928, F₃, 5, 9) (dual of [(4928, 5), 24581, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 8, F₃, 5, 4) (dual of [(8, 5), 35, 5]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(3⁵, 8, F₃, 4, 4) (dual of [(8, 4), 27, 5]-NRT-code), using
      - appending kth column [i] based on 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(3⁵⁴, 4920, F₃, 5, 9) (dual of [(4920, 5), 24546, 10]-NRT-code), using
    - OOA 4-folding and stacking with additional row [i] based on linear OA(3⁵⁴, 19681, F₃, 9) (dual of [19681, 19627, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁵⁴, 19682, F₃, 9) (dual of [19682, 19628, 10]-code), using
        the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
linear OOA(3¹⁸⁰, 1677720, F₃, 5, 18) (dual of [(1677720, 5), 8388420, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁸⁰, 8388600, F₃, 18) (dual of [8388600, 8388420, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.