MinT - Information on Result #1022151

Information on Result #1022151

Linear OOA(64³⁷, 5854656, F₆₄, 3, 7) (dual of [(5854656, 3), 17563931, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 3, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64⁰, 91479, F₆₄, 3, 0) (dual of [(91479, 3), 274437, 1]-NRT-code) (see above)
linear OOA(64¹, 91479, F₆₄, 3, 1) (dual of [(91479, 3), 274436, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [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, 91479, F₆₄, 3, 1) (dual of [(91479, 3), 274436, 2]-NRT-code) (see above)
linear OOA(64¹, 91479, F₆₄, 3, 1) (dual of [(91479, 3), 274436, 2]-NRT-code) (see above)
linear OOA(64¹, 91479, F₆₄, 3, 1) (dual of [(91479, 3), 274436, 2]-NRT-code) (see above)
linear OOA(64⁴, 91479, F₆₄, 3, 2) (dual of [(91479, 3), 274433, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁴, 266305, F₆₄, 3, 2) (dual of [(266305, 3), 798911, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(64⁴, 266305, F₆₄, 2, 2) (dual of [(266305, 2), 532606, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(64⁴, 266305, F₆₄, 2) (dual of [266305, 266301, 3]-code), using
      - Hamming code H(4,64) [i]
linear OOA(64⁶, 91479, F₆₄, 3, 3) (dual of [(91479, 3), 274431, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁶, 270401, F₆₄, 3, 3) (dual of [(270401, 3), 811197, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(64⁶, 270402, F₆₄, 3) (dual of [270402, 270396, 4]-code or 270402-cap in PG(5,64)), using
    - large caps in PG(5,Â b) [i]
linear OOA(64²³, 91479, F₆₄, 3, 7) (dual of [(91479, 3), 274414, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁴, 4097, F₆₄, 3, 3) (dual of [(4097, 3), 12287, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(64⁴, 4097, F₆₄, 2, 3) (dual of [(4097, 2), 8190, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
        ovoid in PG(3,Â 64) [i]
  2. linear OOA(64¹⁹, 87382, F₆₄, 3, 7) (dual of [(87382, 3), 262127, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64¹⁹, 262146, F₆₄, 7) (dual of [262146, 262127, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹⁹, 262147, F₆₄, 7) (dual of [262147, 262128, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(64¹⁹, 262144, F₆₄, 7) (dual of [262144, 262125, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(64¹⁶, 262144, F₆₄, 6) (dual of [262144, 262128, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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 s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.