MinT - Information on Result #1018547

Information on Result #1018547

Linear OOA(81⁶⁴, 5605684, F₈₁, 3, 10) (dual of [(5605684, 3), 16816988, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁷, 4194301, F₈₁, 3, 5) (dual of [(4194301, 3), 12582886, 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(81⁴⁷, 2802842, F₈₁, 3, 10) (dual of [(2802842, 3), 8408479, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81¹⁰, 6641, F₈₁, 3, 5) (dual of [(6641, 3), 19913, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(81¹⁰, 6642, F₈₁, 2, 5) (dual of [(6642, 2), 13274, 6]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 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, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
        linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 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, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
        linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
        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(81⁵, 82, F₈₁, 2, 5) (dual of [(82, 2), 159, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;159,81) [i]
  2. linear OOA(81³⁷, 2796201, F₈₁, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’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.