MinT - Information on Result #563483

Information on Result #563483

There is no linear OOA(8¹⁵⁷, 173, F₈, 2, 137) (dual of [(173, 2), 189, 138]-NRT-code), because 1 step m-reduction would yield linear OA(8¹⁵⁶, 173, F₈, 136) (dual of [173, 17, 137]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(8¹⁵⁵, 161, F₈, 136) (dual of [161, 6, 137]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(8¹⁵⁴, 157, F₈, 136) (dual of [157, 3, 137]-code), but
      - Griesmer bound [i]
    2. OA(8⁶, 161, S₈, 4), but
      - discarding factors would yield OA(8⁶, 104, S₈, 4), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 263173 > 8⁶ [i]
2. OA(8¹⁷, 173, S₈, 12), but
  - discarding factors would yield OA(8¹⁷, 158, S₈, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 2322 300560 650316 > 8¹⁷ [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(8¹⁵⁷, 173, F₈, 3, 137) (dual of [(173, 3), 362, 138]-NRT-code)	[i]		Depth Reduction