MinT - Information on Result #1082439

Information on Result #1082439

Linear OOA(81⁷³, 4732462, F₈₁, 4, 11) (dual of [(4732462, 4), 18929775, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁷, 4194301, F₈₁, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(81¹⁷, large, F₈₁, 5) (dual of [large, large−17, 6]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
linear OOA(81⁵⁶, 2366231, F₈₁, 4, 11) (dual of [(2366231, 4), 9464868, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81¹⁵, 269081, F₈₁, 4, 5) (dual of [(269081, 4), 1076309, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(81¹⁵, 269082, F₈₁, 2, 5) (dual of [(269082, 2), 538149, 6]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
        linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
        linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
        linear OOA(81³, 3322, F₈₁, 2, 2) (dual of [(3322, 2), 6641, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
        appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
        linear OOA(81⁹, 3322, F₈₁, 2, 5) (dual of [(3322, 2), 6635, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;162,81) [i]
        linear OOA(81⁷, 3240, F₈₁, 2, 5) (dual of [(3240, 2), 6473, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁷, 6480, F₈₁, 5) (dual of [6480, 6473, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(81⁴¹, 2097150, F₈₁, 4, 11) (dual of [(2097150, 4), 8388559, 12]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(81⁴¹, 8388600, F₈₁, 11) (dual of [8388600, 8388559, 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.