MinT - Information on Result #1021447

Information on Result #1021447

Linear OOA(5⁷⁸, large, F₅, 3, 7), using generalized (u,Â u+v)-construction based on

linear OOA(5¹, 2441406, F₅, 3, 1) (dual of [(2441406, 3), 7324217, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(5¹, 2441406, F₅, 3, 1) (dual of [(2441406, 3), 7324217, 2]-NRT-code) (see above)
linear OOA(5¹⁰, 2441406, F₅, 3, 2) (dual of [(2441406, 3), 7324208, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(5¹⁰, 2441406, F₅, 2, 2) (dual of [(2441406, 2), 4882802, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(5¹⁰, 2441406, F₅, 2) (dual of [2441406, 2441396, 3]-code), using
    - Hamming code H(10,5) [i]
linear OOA(5¹⁵, 2796201, F₅, 3, 3) (dual of [(2796201, 3), 8388588, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5¹⁵, 3050325, F₅, 3, 3) (dual of [(3050325, 3), 9150960, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(5¹⁵, 3050326, F₅, 3) (dual of [3050326, 3050311, 4]-code or 3050326-cap in PG(14,5)), using
    - product of projective cap with cap in AG(6,Â 5) [i] based on linear OA(5⁹, 4700, F₅, 3) (dual of [4700, 4691, 4]-code or 4700-cap in PG(8,5)), using
      - caps completed using a computer search [i]
linear OOA(5⁵¹, 2796201, F₅, 3, 7) (dual of [(2796201, 3), 8388552, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁵¹, large, F₅, 7) (dual of [large, large−51, 8]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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		Method
1	Linear OOA(5⁷⁸, large, F₅, 3, 6)	[i]	Strength Reduction for OOAs
2	Linear OOA(5⁷⁸, large, F₅, 3, 5)	[i]
3	Linear OOA(5⁷⁸, large, F₅, 3, 4)	[i]
4	Linear OOA(5⁷⁸, large, F₅, 3, 3)	[i]