MinT - Information on Result #1017834

Information on Result #1017834

Linear OOA(64⁵⁰, 87512, F₆₄, 3, 14) (dual of [(87512, 3), 262486, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁰, 130, F₆₄, 3, 7) (dual of [(130, 3), 380, 8]-NRT-code), using
- (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(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(64⁴⁰, 87382, F₆₄, 3, 14) (dual of [(87382, 3), 262106, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁴⁰, 262146, F₆₄, 14) (dual of [262146, 262106, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁴⁰, 262147, F₆₄, 14) (dual of [262147, 262107, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. linear OA(64⁴⁰, 262144, F₆₄, 14) (dual of [262144, 262104, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(64³⁷, 262144, F₆₄, 13) (dual of [262144, 262107, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. 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, 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.