MinT - Information on Result #900482

Information on Result #900482

Linear OOA(27⁵⁹, 4204144, F₂₇, 2, 10) (dual of [(4204144, 2), 8408229, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27¹³, 9843, F₂₇, 2, 5) (dual of [(9843, 2), 19673, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27¹³, 19686, F₂₇, 5) (dual of [19686, 19673, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(27¹³, 19683, F₂₇, 5) (dual of [19683, 19670, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(27¹⁰, 19683, F₂₇, 4) (dual of [19683, 19673, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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]
linear OOA(27⁴⁶, 4194301, F₂₇, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁴⁶, 8388602, F₂₇, 10) (dual of [8388602, 8388556, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁴⁶, large, F₂₇, 10) (dual of [large, large−46, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.