MinT - Information on Result #2613317

Information on Result #2613317

Linear OOA(2¹⁵², 60, F₂, 3, 78) (dual of [(60, 3), 28, 79]-NRT-code), using strength reduction based on linear OOA(2¹⁵², 60, F₂, 3, 79) (dual of [(60, 3), 28, 80]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁴⁶, 20, F₄, 3, 39) (dual of [(20, 3), 14, 40]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴⁶, 21, F₄, 3, 39) (dual of [(21, 3), 17, 40]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,23P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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(2¹⁵³, 60, F₂, 3, 78) (dual of [(60, 3), 27, 79]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁵², 30, F₂, 6, 78) (dual of [(30, 6), 28, 79]-NRT-code)	[i]		OOA Folding