MinT - Information on Result #1017978

Information on Result #1017978

Linear OOA(64⁵⁰, 1526, F₆₄, 3, 18) (dual of [(1526, 3), 4528, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁵, 160, F₆₄, 3, 9) (dual of [(160, 3), 465, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁵, 80, F₆₄, 3, 4) (dual of [(80, 3), 235, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,235P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(64¹⁰, 80, F₆₄, 3, 9) (dual of [(80, 3), 230, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,230P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80 (see above)
linear OOA(64³⁵, 1366, F₆₄, 3, 18) (dual of [(1366, 3), 4063, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64³⁵, 4098, F₆₄, 18) (dual of [4098, 4063, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(64³⁵, 4096, F₆₄, 18) (dual of [4096, 4061, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(64³³, 4096, F₆₄, 17) (dual of [4096, 4063, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.