MinT - Information on Result #1195363

Information on Result #1195363

Linear OOA(16⁸⁵, 131077, F₁₆, 18, 17) (dual of [(131077, 18), 2359301, 18]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OOA(16⁸⁵, 524309, F₁₆, 2, 17) (dual of [(524309, 2), 1048533, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(16⁸⁵, 524312, F₁₆, 2, 17) (dual of [(524312, 2), 1048539, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(16⁹, 24, F₁₆, 2, 8) (dual of [(24, 2), 39, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,39P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(16⁷⁶, 524288, F₁₆, 2, 17) (dual of [(524288, 2), 1048500, 18]-NRT-code), using
    - OOA 2-folding [i] based on 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]

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 (68, 85, 131077)-net over F₁₆	[i]		Net Defined by OOA