MinT - Information on Result #1204280

Information on Result #1204280

Digital (19, 27, 2097407)-net over F₂₅₆, using net defined by OOA based on linear OOA(256²⁷, 2097407, F₂₅₆, 12, 8) (dual of [(2097407, 12), 25168857, 9]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(256²⁷, 2097408, F₂₅₆, 4, 8) (dual of [(2097408, 4), 8389605, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁵, 258, F₂₅₆, 4, 4) (dual of [(258, 4), 1027, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(256⁵, 258, F₂₅₆, 3, 4) (dual of [(258, 3), 769, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (1, 5, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256²², 2097150, F₂₅₆, 4, 8) (dual of [(2097150, 4), 8388578, 9]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(256²², 8388600, F₂₅₆, 8) (dual of [8388600, 8388578, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(256²², large, F₂₅₆, 8) (dual of [large, large−22, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,7], 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, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (46, 54, 4194814)-net over F₁₆	[i]		Trace Code for Nets