MinT - Information on Result #2518977

Information on Result #2518977

Linear OOA(27⁹⁰, large, F₂₇, 2, 12), using 4 times NRT-code embedding in larger space based on linear OOA(27⁸², 8388602, F₂₇, 2, 12) (dual of [(8388602, 2), 16777122, 13]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(27²⁶, 4194301, F₂₇, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27²⁶, 8388602, F₂₇, 6) (dual of [8388602, 8388576, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(27²⁶, large, F₂₇, 6) (dual of [large, large−26, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
2. linear OOA(27⁵⁶, 4194301, F₂₇, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27⁵⁶, 8388602, F₂₇, 12) (dual of [8388602, 8388546, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁵⁶, large, F₂₇, 12) (dual of [large, large−56, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(27⁹¹, large, F₂₇, 2, 12)	[i]		OOA Duplication