MinT - Information on Result #900609

Information on Result #900609

Linear OOA(27⁶³, 265778, F₂₇, 2, 14) (dual of [(265778, 2), 531493, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27¹⁰, 56, F₂₇, 2, 7) (dual of [(56, 2), 102, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(27³, 28, F₂₇, 2, 3) (dual of [(28, 2), 53, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;53,27) [i]
  2. linear OOA(27⁷, 28, F₂₇, 2, 7) (dual of [(28, 2), 49, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;49,27) [i]
linear OOA(27⁵³, 265722, F₂₇, 2, 14) (dual of [(265722, 2), 531391, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁵³, 531444, F₂₇, 14) (dual of [531444, 531391, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁵³, 531445, F₂₇, 14) (dual of [531445, 531392, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. linear OA(27⁵³, 531441, F₂₇, 14) (dual of [531441, 531388, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(27⁴⁹, 531441, F₂₇, 13) (dual of [531441, 531392, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(27⁰, 4, F₂₇, 0) (dual of [4, 4, 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.