MinT - Information on Result #548638

Information on Result #548638

There is no linear OA(7²¹, 35, F₇, 18) (dual of [35, 14, 19]-code), because constructionÂ Y1 would yield

linear OA(7²⁰, 23, F₇, 18) (dual of [23, 3, 19]-code), but
- â€œHi4â€ bound on codes from Brouwerâ€™s database [i]
linear OA(7¹⁴, 35, F₇, 12) (dual of [35, 21, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(7¹⁴, 30, F₇, 12) (dual of [30, 16, 13]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(7¹³, 16, F₇, 12) (dual of [16, 3, 13]-code), but
      - bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
    2. linear OA(7¹⁶, 30, F₇, 14) (dual of [30, 14, 15]-code), but
      - discarding factors / shortening the dual code would yield linear OA(7¹⁶, 24, F₇, 14) (dual of [24, 8, 15]-code), but
        residual code [i] would yield OA(7², 9, S₇, 2), but
        bound for OAs with strength kÂ =Â 2 [i]
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 55 > 7² [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(7²², 36, F₇, 19) (dual of [36, 14, 20]-code)	[i]	Truncation
2	No linear OA(7²³, 37, F₇, 20) (dual of [37, 14, 21]-code)	[i]	Truncation
3	No linear OOA(7²², 35, F₇, 2, 19) (dual of [(35, 2), 48, 20]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(7²³, 35, F₇, 2, 20) (dual of [(35, 2), 47, 21]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(7²¹, 35, F₇, 2, 18) (dual of [(35, 2), 49, 19]-NRT-code)	[i]	Depth Reduction
6	No linear OOA(7²¹, 35, F₇, 3, 18) (dual of [(35, 3), 84, 19]-NRT-code)	[i]	Depth Reduction
7	No digital (3, 21, 35)-net over F₇	[i]	Extracting Embedded Orthogonal Array