MinT - Information on Result #1204512

Information on Result #1204512

Digital (41, 53, 2796201)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁵³, 2796201, F₂₅₆, 15, 12) (dual of [(2796201, 15), 41942962, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(256⁵³, 5592403, F₂₅₆, 3, 12) (dual of [(5592403, 3), 16777156, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(256⁵⁰, 5592402, F₂₅₆, 3, 12) (dual of [(5592402, 3), 16777156, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256¹⁶, 2796201, F₂₅₆, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OOA(256³⁴, 2796201, F₂₅₆, 3, 12) (dual of [(2796201, 3), 8388569, 13]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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 (94, 106, 5592402)-net over F₁₆	[i]		Trace Code for Nets