MinT - Information on Result #2226667

Information on Result #2226667

Linear OA(2²²⁶, 412, F₂, 56) (dual of [412, 186, 57]-code), using 1 times truncation based on linear OA(2²²⁷, 413, F₂, 57) (dual of [413, 186, 58]-code), using

concatenation of two codes [i] based on
1. linear OA(64²⁸, 59, F₆₄, 28) (dual of [59, 31, 29]-code or 59-arc in PG(27,64)), using
  - discarding factors / shortening the dual code based on linear OA(64²⁸, 64, F₆₄, 28) (dual of [64, 36, 29]-code or 64-arc in PG(27,64)), using
    - Reedâ€“Solomon code RS(36,64) [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(2²²⁶, 206, F₂, 2, 56) (dual of [(206, 2), 186, 57]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²²⁶, 137, F₂, 3, 56) (dual of [(137, 3), 185, 57]-NRT-code)	[i]		OOA Folding