MinT - Information on Result #1022469

Information on Result #1022469

Linear OOA(64⁶⁴, 1561, F₆₄, 3, 23) (dual of [(1561, 3), 4619, 24]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁹, 195, F₆₄, 3, 11) (dual of [(195, 3), 566, 12]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64³, 65, F₆₄, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;192,64) [i]
  2. linear OOA(64⁵, 65, F₆₄, 3, 5) (dual of [(65, 3), 190, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;190,64) [i]
  3. linear OOA(64¹¹, 65, F₆₄, 3, 11) (dual of [(65, 3), 184, 12]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;184,64) [i]
linear OOA(64⁴⁵, 1366, F₆₄, 3, 23) (dual of [(1366, 3), 4053, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁴⁵, 4098, F₆₄, 23) (dual of [4098, 4053, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
    1. linear OA(64⁴⁵, 4096, F₆₄, 23) (dual of [4096, 4051, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(64⁴³, 4096, F₆₄, 22) (dual of [4096, 4053, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 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, 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.