MinT - Information on Result #1130652

Information on Result #1130652

Linear OOA(256³⁹, 1775640, F₂₅₆, 6, 10) (dual of [(1775640, 6), 10653801, 11]-NRT-code), using OOA stacking with additional row based on linear OOA(256³⁹, 1775641, F₂₅₆, 5, 10) (dual of [(1775641, 5), 8878166, 11]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(256¹¹, 97921, F₂₅₆, 5, 5) (dual of [(97921, 5), 489594, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(256¹¹, 195843, F₂₅₆, 5) (dual of [195843, 195832, 6]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(256¹, 65281, F₂₅₆, 1) (dual of [65281, 65280, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OA(256³, 65281, F₂₅₆, 2) (dual of [65281, 65278, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(256³, 65793, F₂₅₆, 2) (dual of [65793, 65790, 3]-code), using
        Hamming code H(3,256) [i]
      3. linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
2. linear OOA(256²⁸, 1677720, F₂₅₆, 5, 10) (dual of [(1677720, 5), 8388572, 11]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(256²⁸, 8388600, F₂₅₆, 10) (dual of [8388600, 8388572, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(256²⁸, large, F₂₅₆, 10) (dual of [large, large−28, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.