MinT - Information on Result #2441891

Information on Result #2441891

Linear OOA(4¹⁸², 135, F₄, 2, 84) (dual of [(135, 2), 88, 85]-NRT-code), using strength reduction based on linear OOA(4¹⁸², 135, F₄, 2, 85) (dual of [(135, 2), 88, 86]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16⁴⁶, 45, F₁₆, 2, 42) (dual of [(45, 2), 44, 43]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,47P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]
2. linear OA(4¹, 3, F₄, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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(4¹⁸⁴, 136, F₄, 2, 84) (dual of [(136, 2), 88, 85]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁸³, 135, F₄, 2, 84) (dual of [(135, 2), 87, 85]-NRT-code)	[i]		OOA Duplication