MinT - Information on Result #548424

Information on Result #548424

There is no linear OA(2²⁴², 253, F₂, 122) (dual of [253, 11, 123]-code), because residual code would yield linear OA(2¹²⁰, 130, F₂, 61) (dual of [130, 10, 62]-code), but

1 times truncation [i] would yield linear OA(2¹¹⁹, 129, F₂, 60) (dual of [129, 10, 61]-code), but
- residual code [i] would yield linear OA(2⁵⁹, 68, F₂, 30) (dual of [68, 9, 31]-code), but
  - adding a parity check bit [i] would yield linear OA(2⁶⁰, 69, F₂, 31) (dual of [69, 9, 32]-code), but
    - â€œBGVâ€ bound on codes from Brouwerâ€™s database [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(2²⁴³, 254, F₂, 123) (dual of [254, 11, 124]-code)	[i]		Truncation
2	No linear OOA(2²⁴², 253, F₂, 2, 122) (dual of [(253, 2), 264, 123]-NRT-code)	[i]		Depth Reduction
3	No linear OOA(2²⁴², 253, F₂, 3, 122) (dual of [(253, 3), 517, 123]-NRT-code)	[i]
4	No linear OOA(2²⁴², 253, F₂, 4, 122) (dual of [(253, 4), 770, 123]-NRT-code)	[i]
5	No linear OOA(2²⁴², 253, F₂, 5, 122) (dual of [(253, 5), 1023, 123]-NRT-code)	[i]
6	No linear OOA(2²⁴², 253, F₂, 6, 122) (dual of [(253, 6), 1276, 123]-NRT-code)	[i]
7	No linear OOA(2²⁴², 253, F₂, 7, 122) (dual of [(253, 7), 1529, 123]-NRT-code)	[i]
8	No linear OOA(2²⁴², 253, F₂, 8, 122) (dual of [(253, 8), 1782, 123]-NRT-code)	[i]