MinT - Information on Result #669360

Information on Result #669360

Linear OA(64²³, 4160, F₆₄, 9) (dual of [4160, 4137, 10]-code), using generalized (u,Â u+v)-construction based on

linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 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]
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
linear OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code), using
- discarding factors / shortening the dual code 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 OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code) (see above)
linear OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code) (see above)
linear OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code) (see above)
linear OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code) (see above)
linear OA(64², 65, F₆₄, 2) (dual of [65, 63, 3]-code or 65-arc in PG(1,64)), using
- extended Reedâ€“Solomon code RS_e(63,64) [i]
- Hamming code H(2,64) [i]
linear OA(64³, 65, F₆₄, 3) (dual of [65, 62, 4]-code or 65-arc in PG(2,64) or 65-cap in PG(2,64)), using
- extended Reedâ€“Solomon code RS_e(62,64) [i]
linear OA(64⁴, 65, F₆₄, 4) (dual of [65, 61, 5]-code or 65-arc in PG(3,64)), using
- extended Reedâ€“Solomon code RS_e(61,64) [i]
linear OA(64⁹, 65, F₆₄, 9) (dual of [65, 56, 10]-code or 65-arc in PG(8,64)), using
- extended Reedâ€“Solomon code RS_e(56,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65Â | 64²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.