MinT - Information on Result #903819

Information on Result #903819

Linear OOA(64⁵⁰, 2209, F₆₄, 2, 18) (dual of [(2209, 2), 4368, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁵, 160, F₆₄, 2, 9) (dual of [(160, 2), 305, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁵, 80, F₆₄, 2, 4) (dual of [(80, 2), 155, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,155P) [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, 2, 9) (dual of [(80, 2), 150, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,150P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80 (see above)
linear OOA(64³⁵, 2049, F₆₄, 2, 18) (dual of [(2049, 2), 4063, 19]-NRT-code), using
- OOA 2-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.