MinT - Information on Result #554938

Information on Result #554938

There is no linear OOA(2²⁵¹, 384, F₂, 2, 115) (dual of [(384, 2), 517, 116]-NRT-code), because 3 step m-reduction would yield linear OA(2²⁴⁸, 384, F₂, 112) (dual of [384, 136, 113]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2²⁴⁷, 332, F₂, 112) (dual of [332, 85, 113]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(2²⁴⁶, 302, S₂, 112), but
      - 2 times truncation [i] would yield OA(2²⁴⁴, 300, S₂, 110), but
        the linear programming bound shows that MÂ â‰¥ 727209 932038 995964 963694 786156 506719 769259 430085 807852 102717 045283 079365 167115 254635 995296 956416 / 21378 491075 472167 578125 > 2²⁴⁴ [i]
    2. linear OA(2⁸⁵, 332, F₂, 30) (dual of [332, 247, 31]-code), but
      - the Johnson bound shows that NÂ â‰¤ 220 247871 551638 926977 652794 793575 888633 238636 124356 543746 403131 692235 320146 < 2²⁴⁷ [i]
2. linear OA(2¹³⁶, 384, F₂, 52) (dual of [384, 248, 53]-code), but
  - discarding factors / shortening the dual code would yield linear OA(2¹³⁶, 374, F₂, 52) (dual of [374, 238, 53]-code), but
    - the improved Johnson bound shows that NÂ â‰¤ 2 360702 811474 389063 749944 041391 364709 858504 534718 295956 994191 765553 370834 < 2²³⁸ [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(2²⁵¹, 384, F₂, 3, 115) (dual of [(384, 3), 901, 116]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(2²⁵¹, 384, F₂, 4, 115) (dual of [(384, 4), 1285, 116]-NRT-code)	[i]		Depth Reduction