MinT - Information on Result #1017381

Information on Result #1017381

Linear OOA(49⁴⁴, 902, F₄₉, 3, 16) (dual of [(902, 3), 2662, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49¹³, 101, F₄₉, 3, 8) (dual of [(101, 3), 290, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49⁴, 50, F₄₉, 3, 4) (dual of [(50, 3), 146, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;146,49) [i]
  2. linear OOA(49⁹, 51, F₄₉, 3, 8) (dual of [(51, 3), 144, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 9, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
linear OOA(49³¹, 801, F₄₉, 3, 16) (dual of [(801, 3), 2372, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(49³¹, 2403, F₄₉, 16) (dual of [2403, 2372, 17]-code), using
  - constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
    1. linear OA(49³¹, 2401, F₄₉, 16) (dual of [2401, 2370, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    2. linear OA(49²⁹, 2401, F₄₉, 15) (dual of [2401, 2372, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    3. linear OA(49⁰, 2, F₄₉, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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.