MinT - Information on Result #2705413

Information on Result #2705413

Linear OOA(81²³, large, F₈₁, 3, 3), using 81¹ times duplication based on linear OOA(81²², large, F₈₁, 3, 3), using

strength reduction [i] based on linear OOA(81²², large, F₈₁, 3, 5), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81², 82, F₈₁, 3, 2) (dual of [(82, 3), 244, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;244,81) [i]
  2. linear OOA(81²⁰, 8388602, F₈₁, 3, 5) (dual of [(8388602, 3), 25165786, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(81²⁰, large, F₈₁, 2, 5), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 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, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
        linear OOA(81¹, 265722, F₈₁, 2, 1) (dual of [(265722, 2), 531443, 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, 265722, F₈₁, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code) (see above)
        linear OOA(81¹, 265722, F₈₁, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code) (see above)
        linear OOA(81⁴, 265722, F₈₁, 2, 2) (dual of [(265722, 2), 531440, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81⁴, 538084, F₈₁, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
        appending kth column [i] based on linear OA(81⁴, 538084, F₈₁, 2) (dual of [538084, 538080, 3]-code), using
        Hamming code H(4,81) [i]
        linear OOA(81¹³, 265722, F₈₁, 2, 5) (dual of [(265722, 2), 531431, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81¹³, 531444, F₈₁, 5) (dual of [531444, 531431, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(81¹³, 531441, F₈₁, 5) (dual of [531441, 531428, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(81¹⁰, 531441, F₈₁, 4) (dual of [531441, 531431, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.