MinT - Information on Result #562204

Information on Result #562204

There is no linear OOA(5²⁸, 64, F₅, 2, 22) (dual of [(64, 2), 100, 23]-NRT-code), because 2 step m-reduction would yield linear OA(5²⁶, 64, F₅, 20) (dual of [64, 38, 21]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(5²⁵, 34, F₅, 20) (dual of [34, 9, 21]-code), but
  - residual code [i] would yield linear OA(5⁵, 13, F₅, 4) (dual of [13, 8, 5]-code), but
    - â€œBouâ€ bound on codes from Brouwerâ€™s database [i]
2. linear OA(5³⁸, 64, F₅, 30) (dual of [64, 26, 31]-code), but
  - discarding factors / shortening the dual code would yield linear OA(5³⁸, 61, F₅, 30) (dual of [61, 23, 31]-code), but
    - constructionÂ Y1 [i] would yield
      1. linear OA(5³⁷, 43, F₅, 30) (dual of [43, 6, 31]-code), but
        residual code [i] would yield linear OA(5⁷, 12, F₅, 6) (dual of [12, 5, 7]-code), but
        a result by Dodunekov and Landjev [i]
      2. OA(5²³, 61, S₅, 18), but
        the linear programming bound shows that MÂ â‰¥ 6321 833259 448409 889221 191406 250000 / 502952 782605 714137 > 5²³ [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OOA(5²⁸, 64, F₅, 3, 22) (dual of [(64, 3), 164, 23]-NRT-code)	[i]		Depth Reduction