MinT - Information on Result #2698951

Information on Result #2698951

Linear OOA(8¹⁰⁹, large, F₈, 3, 9), using 6 times NRT-code embedding in larger space based on linear OOA(8⁹¹, large, F₈, 3, 9), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8²⁵, 4194301, F₈, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(8²⁵, 8388602, F₈, 4) (dual of [8388602, 8388577, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(8²⁵, large, F₈, 4) (dual of [large, large−25, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
2. linear OOA(8⁶⁶, 5592402, F₈, 3, 9) (dual of [(5592402, 3), 16777140, 10]-NRT-code), using
  - trace code [i] based on linear OOA(64³³, 2796201, F₆₄, 3, 9) (dual of [(2796201, 3), 8388570, 10]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64³³, large, F₆₄, 9) (dual of [large, large−33, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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(8¹¹⁰, large, F₈, 3, 9)	[i]		OOA Duplication
2	Linear OOA(8¹¹¹, large, F₈, 3, 9)	[i]		OOA Duplication