MinT - Information on Result #901079

Information on Result #901079

Linear OOA(27⁹⁹, 9939, F₂₇, 2, 26) (dual of [(9939, 2), 19779, 27]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27²³, 96, F₂₇, 2, 13) (dual of [(96, 2), 169, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(27⁸, 48, F₂₇, 2, 6) (dual of [(48, 2), 88, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,89P) [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]
  2. linear OOA(27¹⁵, 48, F₂₇, 2, 13) (dual of [(48, 2), 81, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,82P) [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48 (see above)
linear OOA(27⁷⁶, 9843, F₂₇, 2, 26) (dual of [(9843, 2), 19610, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁷⁶, 19686, F₂₇, 26) (dual of [19686, 19610, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
    1. linear OA(27⁷⁶, 19683, F₂₇, 26) (dual of [19683, 19607, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(27⁷³, 19683, F₂₇, 25) (dual of [19683, 19610, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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.