MinT - Information on Result #1013081

Information on Result #1013081

Linear OOA(5¹¹³, 4196704, F₅, 3, 10) (dual of [(4196704, 3), 12589999, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5²¹, 2403, F₅, 3, 5) (dual of [(2403, 3), 7188, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(5²¹, 2404, F₅, 2, 5) (dual of [(2404, 2), 4787, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code) (see above)
    3. linear OOA(5⁵, 601, F₅, 2, 2) (dual of [(601, 2), 1197, 3]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(5⁵, 781, F₅, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
        appending kth column [i] based on linear OA(5⁵, 781, F₅, 2) (dual of [781, 776, 3]-code), using
        Hamming code H(5,5) [i]
    4. 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(5⁹², 4194301, F₅, 3, 10) (dual of [(4194301, 3), 12582811, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(5⁹², 8388602, F₅, 2, 10) (dual of [(8388602, 2), 16777112, 11]-NRT-code), using
  - trace code [i] based on linear OOA(25⁴⁶, 4194301, F₂₅, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁴⁶, 8388602, F₂₅, 10) (dual of [8388602, 8388556, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁴⁶, large, F₂₅, 10) (dual of [large, large−46, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’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.