MinT - Information on Result #1021278

Information on Result #1021278

Linear OOA(4¹⁹, 71, F₄, 3, 7) (dual of [(71, 3), 194, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4¹, 17, F₄, 3, 1) (dual of [(17, 3), 50, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹, s, F₄, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [i] based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(4³, 17, F₄, 3, 2) (dual of [(17, 3), 48, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4³, 21, F₄, 3, 2) (dual of [(21, 3), 60, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(4³, 21, F₄, 2, 2) (dual of [(21, 2), 39, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
      - Hamming code H(3,4) [i]
linear OOA(4⁴, 17, F₄, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
    - ovoid in PG(3,Â 4) [i]
linear OOA(4¹¹, 20, F₄, 3, 7) (dual of [(20, 3), 49, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 11, 20)-net over F₄, using
  - linear code embedding found in a computer search [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4¹⁵², 2796272, F₄, 3, 15) (dual of [(2796272, 3), 8388664, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(4¹⁴⁰, 2796272, F₄, 3, 14) (dual of [(2796272, 3), 8388676, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(4¹⁹, 70, F₄, 9, 7) (dual of [(70, 9), 611, 8]-NRT-code)	[i]	OOA Stacking with Additional Row