MinT - Information on Result #1022490

Information on Result #1022490

Linear OOA(64⁴¹, 1561, F₆₄, 3, 15) (dual of [(1561, 3), 4642, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹², 195, F₆₄, 3, 7) (dual of [(195, 3), 573, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64², 65, F₆₄, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;193,64) [i]
  2. 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]
  3. linear OOA(64⁷, 65, F₆₄, 3, 7) (dual of [(65, 3), 188, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;188,64) [i]
linear OOA(64²⁹, 1366, F₆₄, 3, 15) (dual of [(1366, 3), 4069, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64²⁹, 4098, F₆₄, 15) (dual of [4098, 4069, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
    1. linear OA(64²⁹, 4096, F₆₄, 15) (dual of [4096, 4067, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(64²⁷, 4096, F₆₄, 14) (dual of [4096, 4069, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.