MinT - Information on Result #902779

Information on Result #902779

Linear OOA(32¹⁰⁸, 641, F₃₂, 2, 39) (dual of [(641, 2), 1174, 40]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32³⁴, 128, F₃₂, 2, 19) (dual of [(128, 2), 222, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32¹², 64, F₃₂, 2, 9) (dual of [(64, 2), 116, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,118P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(32²², 64, F₃₂, 2, 19) (dual of [(64, 2), 106, 20]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,108P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64 (see above)
linear OOA(32⁷⁴, 513, F₃₂, 2, 39) (dual of [(513, 2), 952, 40]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁷⁴, 1026, F₃₂, 39) (dual of [1026, 952, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(37) [i] based on
    1. linear OA(32⁷⁴, 1024, F₃₂, 39) (dual of [1024, 950, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    2. linear OA(32⁷², 1024, F₃₂, 38) (dual of [1024, 952, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
    3. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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.