MinT - Information on Result #2699045

Information on Result #2699045

Linear OOA(8¹²², large, F₈, 3, 10), using 5 times NRT-code embedding in larger space based on linear OOA(8¹⁰⁷, large, F₈, 3, 10), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8³³, 4194301, F₈, 3, 5) (dual of [(4194301, 3), 12582870, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(8³³, large, F₈, 5) (dual of [large, large−33, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
2. linear OOA(8⁷⁴, 5592402, F₈, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
  - trace code [i] based on linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(8¹²³, large, F₈, 3, 10)	[i]		OOA Duplication
2	Linear OOA(8¹²⁴, large, F₈, 3, 10)	[i]		OOA Duplication