MinT - Information on Result #1020118

Information on Result #1020118

Linear OOA(256⁵⁷, 2818048, F₂₅₆, 3, 15) (dual of [(2818048, 3), 8454087, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁴, 21847, F₂₅₆, 3, 7) (dual of [(21847, 3), 65527, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(256¹⁴, 65541, F₂₅₆, 7) (dual of [65541, 65527, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(256¹⁴, 65542, F₂₅₆, 7) (dual of [65542, 65528, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(256¹³, 65537, F₂₅₆, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(256⁹, 65537, F₂₅₆, 5) (dual of [65537, 65528, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 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]
linear OOA(256⁴³, 2796201, F₂₅₆, 3, 15) (dual of [(2796201, 3), 8388560, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.