MinT - Information on Result #2796593

Information on Result #2796593

Linear OOA(3⁸¹, large, F₃, 4, 5), using 5 times NRT-code embedding in larger space based on linear OOA(3⁶¹, large, F₃, 4, 5), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3¹, 2391484, F₃, 4, 1) (dual of [(2391484, 4), 9565935, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
    - appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
2. linear OOA(3¹⁴, 2391484, F₃, 4, 2) (dual of [(2391484, 4), 9565922, 3]-NRT-code), using
  - appending 2 arbitrary columns [i] based on linear OOA(3¹⁴, 2391484, F₃, 2, 2) (dual of [(2391484, 2), 4782954, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(3¹⁴, 2391484, F₃, 2) (dual of [2391484, 2391470, 3]-code), using
      - Hamming code H(14,3) [i]
3. linear OOA(3⁴⁶, 4194301, F₃, 4, 5) (dual of [(4194301, 4), 16777158, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(3⁸², large, F₃, 4, 5)	[i]		OOA Duplication
2	Linear OOA(3⁸³, large, F₃, 4, 5)	[i]		OOA Duplication