MinT - Information on Result #1117250

Information on Result #1117250

Linear OOA(3¹⁸⁰, 4194458, F₃, 5, 11) (dual of [(4194458, 5), 20972110, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁶, 157, F₃, 5, 5) (dual of [(157, 5), 769, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁶, 157, F₃, 4, 5) (dual of [(157, 4), 612, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3¹, 40, F₃, 4, 1) (dual of [(40, 4), 159, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OOA(3⁴, 40, F₃, 4, 2) (dual of [(40, 4), 156, 3]-NRT-code), using
      - appending 2 arbitrary columns [i] based on linear OOA(3⁴, 40, F₃, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
        appending kth column [i] based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]
    3. linear OOA(3¹¹, 77, F₃, 4, 5) (dual of [(77, 4), 297, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (6, 11, 77)-net over F₃, using
        linear code embedding found in a computer search [i]
linear OOA(3¹⁶⁴, 4194301, F₃, 5, 11) (dual of [(4194301, 5), 20971341, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁶⁴, 8388602, F₃, 3, 11) (dual of [(8388602, 3), 25165642, 12]-NRT-code), using
  - trace code [i] based on linear OOA(9⁸², 4194301, F₉, 3, 11) (dual of [(4194301, 3), 12582821, 12]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(9⁸², 8388602, F₉, 2, 11) (dual of [(8388602, 2), 16777122, 12]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴¹, 4194301, F₈₁, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴¹, 8388602, F₈₁, 11) (dual of [8388602, 8388561, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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.