MinT - Information on Result #2851701

Information on Result #2851701

Linear OOA(3¹³⁶, large, F₃, 5, 5), using strength reduction based on linear OOA(3¹³⁶, large, F₃, 5, 9), 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(3¹³², 8388599, F₃, 5, 9) (dual of [(8388599, 5), 41942863, 10]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3¹³², 8388600, F₃, 4, 9) (dual of [(8388600, 4), 33554268, 10]-NRT-code), using
    - trace code [i] based on linear OOA(81³³, 2097150, F₈₁, 4, 9) (dual of [(2097150, 4), 8388567, 10]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(81³³, 8388600, F₈₁, 9) (dual of [8388600, 8388567, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(81³³, large, F₈₁, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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(3¹³⁷, large, F₃, 5, 5)	[i]		OOA Duplication
2	Linear OOA(3¹³⁸, large, F₃, 5, 5)	[i]
3	Linear OOA(3¹³⁹, large, F₃, 5, 5)	[i]
4	Linear OOA(3¹⁴⁰, large, F₃, 5, 5)	[i]