MinT - Information on Result #1200711

Information on Result #1200711

Linear OOA(49³⁶, 351, F₄₉, 14, 14) (dual of [(351, 14), 4878, 15]-NRT-code), using OA 7-folding and stacking based on linear OA(49³⁶, 2457, F₄₉, 14) (dual of [2457, 2421, 15]-code), using

discarding factors / shortening the dual code based on linear OA(49³⁶, 2458, F₄₉, 14) (dual of [2458, 2422, 15]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(49⁹, 55, F₄₉, 7) (dual of [55, 46, 8]-code), using
    - constructionÂ X applied to AG(F,14P) âŠ‚ AG(F,15P) [i] based on
      1. linear OA(49⁷, 50, F₄₉, 7) (dual of [50, 43, 8]-code or 50-arc in PG(6,49)), using algebraic-geometric code AG(F,21P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using the rational function field F₄₉(x) [i]
      2. linear OA(49⁴, 50, F₄₉, 4) (dual of [50, 46, 5]-code or 50-arc in PG(3,49)), using algebraic-geometric code AG(F, Q+21P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
      3. linear OA(49², 5, F₄₉, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,49)), using
        discarding factors / shortening the dual code based on linear OA(49², 49, F₄₉, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
        Reedâ€“Solomon code RS(47,49) [i]
  2. linear OA(49²⁷, 2403, F₄₉, 14) (dual of [2403, 2376, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. linear OA(49²⁷, 2401, F₄₉, 14) (dual of [2401, 2374, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. 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]
      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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (22, 36, 351)-net over F₄₉	[i]		Net Defined by OOA