MinT - Information on Result #2416843

Information on Result #2416843

Linear OOA(2⁴⁶, 30, F₂, 2, 22) (dual of [(30, 2), 14, 23]-NRT-code), using strength reduction based on linear OOA(2⁴⁶, 30, F₂, 2, 23) (dual of [(30, 2), 14, 24]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4¹³, 10, F₄, 2, 11) (dual of [(10, 2), 7, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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(2⁴⁶, 15, F₂, 4, 22) (dual of [(15, 4), 14, 23]-NRT-code)	[i]		OOA Folding