MinT - Information on Result #2657470

Information on Result #2657470

Linear OOA(2²⁰⁹, 111, F₂, 3, 74) (dual of [(111, 3), 124, 75]-NRT-code), using 1 step truncation based on linear OOA(2²¹⁰, 112, F₂, 3, 75) (dual of [(112, 3), 126, 76]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁴², 28, F₈, 3, 37) (dual of [(28, 3), 42, 38]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,46P) [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, 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(2²⁰⁹, 55, F₂, 5, 74) (dual of [(55, 5), 66, 75]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁰⁹, 55, F₂, 6, 74) (dual of [(55, 6), 121, 75]-NRT-code)	[i]		OOA Folding