MinT - Information on Result #2226503

Information on Result #2226503

Linear OA(2²¹⁸, 353, F₂, 58) (dual of [353, 135, 59]-code), using 1 times truncation based on linear OA(2²¹⁹, 354, F₂, 59) (dual of [354, 135, 60]-code), using

concatenation of two codes [i] based on
1. linear OA(32³², 59, F₃₂, 29) (dual of [59, 27, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(32³², 63, F₃₂, 29) (dual of [63, 31, 30]-code), using
    - algebraic-geometric code AG(F,33P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 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, 176, F₂, 2, 58) (dual of [(176, 2), 134, 59]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²¹⁸, 117, F₂, 3, 58) (dual of [(117, 3), 133, 59]-NRT-code)	[i]		OOA Folding