MinT - Information on Result #2518531

Information on Result #2518531

Linear OOA(27³², large, F₂₇, 2, 5), using 2 times NRT-code embedding in larger space based on linear OOA(27²⁸, large, F₂₇, 2, 5), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(27¹, 4194301, F₂₇, 2, 1) (dual of [(4194301, 2), 8388601, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
2. linear OOA(27⁶, 4194301, F₂₇, 2, 2) (dual of [(4194301, 2), 8388596, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27⁶, large, F₂₇, 2, 2), using
    - appending kth column [i] based on linear OA(27⁶, large, F₂₇, 2) (dual of [large, large−6, 3]-code), using
      - Hamming code H(6,27) [i]
3. linear OOA(27²¹, 4194301, F₂₇, 2, 5) (dual of [(4194301, 2), 8388581, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27²¹, 8388602, F₂₇, 5) (dual of [8388602, 8388581, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(27²¹, large, F₂₇, 5) (dual of [large, large−21, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (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(27³³, large, F₂₇, 2, 5)	[i]		OOA Duplication