MinT - Information on Result #1013140

Information on Result #1013140

Linear OOA(5¹¹⁸, 4194907, F₅, 3, 11) (dual of [(4194907, 3), 12584603, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁶, 606, F₅, 3, 5) (dual of [(606, 3), 1802, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(5¹⁶, 607, F₅, 2, 5) (dual of [(607, 2), 1198, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(5², 6, F₅, 2, 2) (dual of [(6, 2), 10, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;10,5) [i]
    2. linear OOA(5¹⁴, 601, F₅, 2, 5) (dual of [(601, 2), 1188, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
        trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(5¹⁰², 4194301, F₅, 3, 11) (dual of [(4194301, 3), 12582801, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(5¹⁰², 8388602, F₅, 2, 11) (dual of [(8388602, 2), 16777102, 12]-NRT-code), using
  - trace code [i] based on linear OOA(25⁵¹, 4194301, F₂₅, 2, 11) (dual of [(4194301, 2), 8388551, 12]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁵¹, 8388602, F₂₅, 11) (dual of [8388602, 8388551, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁵¹, large, F₂₅, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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.