MinT - Information on Result #899631

Information on Result #899631

Linear OOA(25⁸⁵, 4194616, F₂₅, 2, 15) (dual of [(4194616, 2), 8389147, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁴, 315, F₂₅, 2, 7) (dual of [(315, 2), 616, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25¹⁴, 630, F₂₅, 7) (dual of [630, 616, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(25¹⁴, 631, F₂₅, 7) (dual of [631, 617, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(25¹³, 626, F₂₅, 7) (dual of [626, 613, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 626Â | 25⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(25⁹, 626, F₂₅, 5) (dual of [626, 617, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 626Â | 25⁴âˆ’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(25¹, 5, F₂₅, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(25⁷¹, 4194301, F₂₅, 2, 15) (dual of [(4194301, 2), 8388531, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷¹, 8388602, F₂₅, 15) (dual of [8388602, 8388531, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁷¹, large, F₂₅, 15) (dual of [large, large−71, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [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.