MinT - Information on Result #1459780

Information on Result #1459780

Linear OOA(27¹⁰⁷, 458800, F₂₇, 2, 27) (dual of [(458800, 2), 917493, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(27¹⁰⁷, 458800, F₂₇, 27) (dual of [458800, 458693, 28]-code), using

discarding factors / shortening the dual code based on linear OA(27¹⁰⁷, 531455, F₂₇, 27) (dual of [531455, 531348, 28]-code), using
- 1 times truncation [i] based on linear OA(27¹⁰⁸, 531456, F₂₇, 28) (dual of [531456, 531348, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(23) [i] based on
    1. linear OA(27¹⁰⁵, 531441, F₂₇, 28) (dual of [531441, 531336, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(27⁹³, 531441, F₂₇, 24) (dual of [531441, 531348, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    3. linear OA(27³, 15, F₂₇, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
      - discarding factors / shortening the dual code based on linear OA(27³, 27, F₂₇, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
        Reedâ€“Solomon code RS(24,27) [i]

Mode: 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(27¹⁰⁷, 65542, F₂₇, 30, 27) (dual of [(65542, 30), 1966153, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row