MinT - Information on Result #2519056

Information on Result #2519056

Linear OOA(27¹⁰⁸, large, F₂₇, 2, 15), using 3 times NRT-code embedding in larger space based on linear OOA(27¹⁰², 8388602, F₂₇, 2, 15) (dual of [(8388602, 2), 16777102, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(27³¹, 4194301, F₂₇, 2, 7) (dual of [(4194301, 2), 8388571, 8]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27³¹, 8388602, F₂₇, 7) (dual of [8388602, 8388571, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(27³¹, large, F₂₇, 7) (dual of [large, large−31, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
2. linear OOA(27⁷¹, 4194301, F₂₇, 2, 15) (dual of [(4194301, 2), 8388531, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27⁷¹, 8388602, F₂₇, 15) (dual of [8388602, 8388531, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁷¹, large, F₂₇, 15) (dual of [large, large−71, 16]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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(27¹⁰⁹, large, F₂₇, 2, 15)	[i]		OOA Duplication