MinT - Information on Result #2417405

Information on Result #2417405

Linear OOA(2⁷², 60, F₂, 2, 24) (dual of [(60, 2), 48, 25]-NRT-code), using strength reduction based on linear OOA(2⁷², 60, F₂, 2, 25) (dual of [(60, 2), 48, 26]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8¹⁴, 15, F₈, 2, 12) (dual of [(15, 2), 16, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁴, 17, F₈, 2, 12) (dual of [(17, 2), 20, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,21P) [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
      - a function field by SÃ©mirat [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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(2⁷², 30, F₂, 4, 24) (dual of [(30, 4), 48, 25]-NRT-code)	[i]		OOA Folding