MinT - Information on Result #1021723

Information on Result #1021723

Linear OOA(7⁷³, large, F₇, 3, 7), using generalized (u,Â u+v)-construction based on

linear OOA(7¹, 960800, F₇, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹, s, F₇, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [i] based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(7¹, 960800, F₇, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code) (see above)
linear OOA(7¹, 960800, F₇, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code) (see above)
linear OOA(7¹, 960800, F₇, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code) (see above)
linear OOA(7⁸, 960800, F₇, 3, 2) (dual of [(960800, 3), 2882392, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(7⁸, 960800, F₇, 2, 2) (dual of [(960800, 2), 1921592, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(7⁸, 960800, F₇, 2) (dual of [960800, 960792, 3]-code), using
    - Hamming code H(8,7) [i]
linear OOA(7¹³, 1921600, F₇, 3, 3) (dual of [(1921600, 3), 5764787, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹³, 6120100, F₇, 3, 3) (dual of [(6120100, 3), 18360287, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(7¹³, 6120101, F₇, 3) (dual of [6120101, 6120088, 4]-code or 6120101-cap in PG(12,7)), using
    - product of projective cap with cap in AG(6,Â 7) [i] based on linear OA(7⁷, 2499, F₇, 3) (dual of [2499, 2492, 4]-code or 2499-cap in PG(6,7)), using
      - product of two caps with tangent hyperplane [i]
linear OOA(7⁴⁸, 1921600, F₇, 3, 7) (dual of [(1921600, 3), 5764752, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁴⁸, 5764800, F₇, 7) (dual of [5764800, 5764752, 8]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,7], 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(7⁷³, large, F₇, 3, 6)	[i]	Strength Reduction for OOAs
2	Linear OOA(7⁷³, large, F₇, 3, 5)	[i]
3	Linear OOA(7⁷³, large, F₇, 3, 4)	[i]
4	Linear OOA(7⁷³, large, F₇, 3, 3)	[i]