MinT - Information on Result #2500281

Information on Result #2500281

Linear OOA(4¹³⁸, 100, F₄, 2, 67) (dual of [(100, 2), 62, 68]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹³⁶, 99, F₄, 2, 67) (dual of [(99, 2), 62, 68]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16³⁵, 33, F₁₆, 2, 33) (dual of [(33, 2), 31, 34]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,32P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [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(4¹³⁹, 100, F₄, 2, 67) (dual of [(100, 2), 61, 68]-NRT-code)	[i]		OOA Duplication