MinT - Information on Result #2226587

Information on Result #2226587

Linear OA(2²¹⁸, 398, F₂, 54) (dual of [398, 180, 55]-code), using 1 times truncation based on linear OA(2²¹⁹, 399, F₂, 55) (dual of [399, 180, 56]-code), using

concatenation of two codes [i] based on
1. linear OA(64²⁷, 57, F₆₄, 27) (dual of [57, 30, 28]-code or 57-arc in PG(26,64)), using
  - discarding factors / shortening the dual code based on linear OA(64²⁷, 64, F₆₄, 27) (dual of [64, 37, 28]-code or 64-arc in PG(26,64)), using
    - Reedâ€“Solomon code RS(37,64) [i]
2. linear OA(2¹, 7, F₂, 1) (dual of [7, 6, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and 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	Linear OOA(2²¹⁸, 199, F₂, 2, 54) (dual of [(199, 2), 180, 55]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²¹⁸, 132, F₂, 3, 54) (dual of [(132, 3), 178, 55]-NRT-code)	[i]		OOA Folding