MinT - Information on Result #902204

Information on Result #902204

Linear OOA(32⁵², 601, F₃₂, 2, 19) (dual of [(601, 2), 1150, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁵, 88, F₃₂, 2, 9) (dual of [(88, 2), 161, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32⁵, 44, F₃₂, 2, 4) (dual of [(44, 2), 83, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,83P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(32¹⁰, 44, F₃₂, 2, 9) (dual of [(44, 2), 78, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,78P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44 (see above)
linear OOA(32³⁷, 513, F₃₂, 2, 19) (dual of [(513, 2), 989, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32³⁷, 1026, F₃₂, 19) (dual of [1026, 989, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
    1. linear OA(32³⁷, 1024, F₃₂, 19) (dual of [1024, 987, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(32³⁵, 1024, F₃₂, 18) (dual of [1024, 989, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.