MinT - Information on Result #1195403

Information on Result #1195403

Linear OOA(16⁹⁶, 116516, F₁₆, 18, 18) (dual of [(116516, 18), 2097192, 19]-NRT-code), using OA 9-folding and stacking based on linear OA(16⁹⁶, 1048644, F₁₆, 18) (dual of [1048644, 1048548, 19]-code), using

discarding factors / shortening the dual code based on linear OA(16⁹⁶, 1048646, F₁₆, 18) (dual of [1048646, 1048550, 19]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16¹⁵, 65, F₁₆, 9) (dual of [65, 50, 10]-code), using
    - extended algebraic-geometric code AG_e(F,55P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]
  2. linear OA(16⁸¹, 1048581, F₁₆, 18) (dual of [1048581, 1048500, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
      1. linear OA(16⁸¹, 1048576, F₁₆, 18) (dual of [1048576, 1048495, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(16⁰, 5, F₁₆, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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 (78, 96, 116516)-net over F₁₆	[i]		Net Defined by OOA