MinT - Information on Result #1017682

Information on Result #1017682

Linear OOA(64⁷⁰, 6124880, F₆₄, 3, 10) (dual of [(6124880, 3), 18374570, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁷, 4194301, F₆₄, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(64¹⁷, large, F₆₄, 5) (dual of [large, large−17, 6]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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(64⁵³, 3062440, F₆₄, 3, 10) (dual of [(3062440, 3), 9187267, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64¹⁶, 266239, F₆₄, 3, 5) (dual of [(266239, 3), 798701, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(64¹⁶, 266240, F₆₄, 2, 5) (dual of [(266240, 2), 532464, 6]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
        linear OOA(64¹, 4160, F₆₄, 2, 1) (dual of [(4160, 2), 8319, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(64¹, 4160, F₆₄, 2, 1) (dual of [(4160, 2), 8319, 2]-NRT-code) (see above)
        linear OOA(64¹, 4160, F₆₄, 2, 1) (dual of [(4160, 2), 8319, 2]-NRT-code) (see above)
        linear OOA(64³, 4160, F₆₄, 2, 2) (dual of [(4160, 2), 8317, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64³, 4161, F₆₄, 2, 2) (dual of [(4161, 2), 8319, 3]-NRT-code), using
        appending kth column [i] based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
        Hamming code H(3,64) [i]
        linear OOA(64¹⁰, 4160, F₆₄, 2, 5) (dual of [(4160, 2), 8310, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s (see above)
        linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
        linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
        linear OOA(64², 65, F₆₄, 2, 2) (dual of [(65, 2), 128, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;128,64) [i]
        linear OOA(64⁵, 65, F₆₄, 2, 5) (dual of [(65, 2), 125, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;125,64) [i]
  2. linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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.