MinT - Information on Result #1170703

Information on Result #1170703

Linear OOA(2⁹⁷, 2097155, F₂, 8, 8) (dual of [(2097155, 8), 16777143, 9]-NRT-code), using appending kth column based on linear OOA(2⁹⁷, 2097155, F₂, 7, 8) (dual of [(2097155, 7), 14679988, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵, 5, F₂, 7, 4) (dual of [(5, 7), 30, 5]-NRT-code), using
  - appending 3 arbitrary columns [i] based on linear OOA(2⁵, 5, F₂, 4, 4) (dual of [(5, 4), 15, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁵, 5, F₂, 3, 4) (dual of [(5, 3), 10, 5]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
2. linear OOA(2⁹², 2097150, F₂, 7, 8) (dual of [(2097150, 7), 14679958, 9]-NRT-code), using
  - OA 4-folding and stacking [i] based on linear OA(2⁹², 8388600, F₂, 8) (dual of [8388600, 8388508, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (89, 97, 2097155)-net over F₂	[i]		Net Defined by OOA