MinT - Information on Result #1144992

Information on Result #1144992

Linear OOA(256⁴³, 1808281, F₂₅₆, 6, 11) (dual of [(1808281, 6), 10849643, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹², 130561, F₂₅₆, 6, 5) (dual of [(130561, 6), 783354, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(256¹², 130562, F₂₅₆, 2, 5) (dual of [(130562, 2), 261112, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(256¹², 261124, F₂₅₆, 5) (dual of [261124, 261112, 6]-code), using
    - generalized (u,Â u+v)-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(256¹, 65281, F₂₅₆, 1) (dual of [65281, 65280, 2]-code) (see above)
      3. 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]
      4. linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(256³¹, 1677720, F₂₅₆, 6, 11) (dual of [(1677720, 6), 10066289, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(256³¹, 8388601, F₂₅₆, 11) (dual of [8388601, 8388570, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(256³¹, large, F₂₅₆, 11) (dual of [large, large−31, 12]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.