MinT - Information on Result #2873414

Information on Result #2873414

Linear OOA(3²¹⁵, large, F₃, 5, 8), using 19 times NRT-code embedding in larger space based on linear OOA(3¹²⁰, large, F₃, 5, 8), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁴, 4, F₃, 5, 4) (dual of [(4, 5), 16, 5]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(5;16,3) [i]
2. linear OOA(3¹¹⁶, 8388599, F₃, 5, 8) (dual of [(8388599, 5), 41942879, 9]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3¹¹⁶, 8388600, F₃, 4, 8) (dual of [(8388600, 4), 33554284, 9]-NRT-code), using
    - trace code [i] based on linear OOA(81²⁹, 2097150, F₈₁, 4, 8) (dual of [(2097150, 4), 8388571, 9]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(81²⁹, 8388600, F₈₁, 8) (dual of [8388600, 8388571, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(81²⁹, large, F₈₁, 8) (dual of [large, large−29, 9]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁶, large, F₃, 5, 8)	[i]		OOA Duplication
2	Linear OOA(3²¹⁷, large, F₃, 5, 8)	[i]
3	Linear OOA(3²¹⁸, large, F₃, 5, 8)	[i]
4	Linear OOA(3²¹⁹, large, F₃, 5, 8)	[i]