MinT - Information on Result #1017320

Information on Result #1017320

Linear OOA(49³⁵, 902, F₄₉, 3, 13) (dual of [(902, 3), 2671, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49¹⁰, 101, F₄₉, 3, 6) (dual of [(101, 3), 293, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49³, 50, F₄₉, 3, 3) (dual of [(50, 3), 147, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;147,49) [i]
  2. linear OOA(49⁷, 51, F₄₉, 3, 6) (dual of [(51, 3), 146, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
linear OOA(49²⁵, 801, F₄₉, 3, 13) (dual of [(801, 3), 2378, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(49²⁵, 2403, F₄₉, 13) (dual of [2403, 2378, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
    1. linear OA(49²⁵, 2401, F₄₉, 13) (dual of [2401, 2376, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(49²³, 2401, F₄₉, 12) (dual of [2401, 2378, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.