MinT - Information on Result #553753

Information on Result #553753

There is no linear OOA(2²⁰⁶, 363, F₂, 2, 89) (dual of [(363, 2), 520, 90]-NRT-code), because 1 step m-reduction would yield linear OA(2²⁰⁵, 363, F₂, 88) (dual of [363, 158, 89]-code), but

constructionÂ Y1 [i] would yield
1. OA(2²⁰⁴, 299, S₂, 88), but
  - adding a parity check bit [i] would yield OA(2²⁰⁵, 300, S₂, 89), but
    - the linear programming bound shows that MÂ â‰¥ 416927 463188 475542 795463 940731 898983 181308 104641 213119 598295 609827 594303 154474 074874 094714 331435 368448 / 5584 401256 756961 297780 513782 298869 514125 > 2²⁰⁵ [i]
2. linear OA(2¹⁵⁸, 363, F₂, 64) (dual of [363, 205, 65]-code), but
  - the improved Johnson bound shows that NÂ â‰¤ 1214 271568 452769 866939 025066 626311 211727 927188 642255 823141 634304 < 2²⁰⁵ [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		Method
1	No linear OOA(2²⁰⁶, 363, F₂, 3, 89) (dual of [(363, 3), 883, 90]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(2²⁰⁶, 363, F₂, 4, 89) (dual of [(363, 4), 1246, 90]-NRT-code)	[i]
3	No linear OOA(2²⁰⁶, 363, F₂, 5, 89) (dual of [(363, 5), 1609, 90]-NRT-code)	[i]
4	No linear OOA(2²⁰⁶, 363, F₂, 6, 89) (dual of [(363, 6), 1972, 90]-NRT-code)	[i]
5	No linear OOA(2²⁰⁶, 363, F₂, 7, 89) (dual of [(363, 7), 2335, 90]-NRT-code)	[i]
6	No linear OOA(2²⁰⁶, 363, F₂, 8, 89) (dual of [(363, 8), 2698, 90]-NRT-code)	[i]