MinT - Information on Result #1197240

Information on Result #1197240

Digital (15, 20, 266478)-net over F₂₇, using net defined by OOA based on linear OOA(27²⁰, 266478, F₂₇, 6, 5) (dual of [(266478, 6), 1598848, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(27²⁰, 266479, F₂₇, 2, 5) (dual of [(266479, 2), 532938, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(27³, 757, F₂₇, 2, 2) (dual of [(757, 2), 1511, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(27³, 757, F₂₇, 2) (dual of [757, 754, 3]-code), using
      - Hamming code H(3,27) [i]
  2. linear OOA(27¹⁷, 265722, F₂₇, 2, 5) (dual of [(265722, 2), 531427, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(27¹⁷, 531444, F₂₇, 5) (dual of [531444, 531427, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(27¹⁷, 531445, F₂₇, 5) (dual of [531445, 531428, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(27¹⁷, 531441, F₂₇, 5) (dual of [531441, 531424, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(27¹³, 531441, F₂₇, 4) (dual of [531441, 531428, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.