MinT - Information on Result #2622703

Information on Result #2622703

Linear OOA(3¹³⁷, 63, F₃, 3, 68) (dual of [(63, 3), 52, 69]-NRT-code), using strength reduction based on linear OOA(3¹³⁷, 63, F₃, 3, 69) (dual of [(63, 3), 52, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9³⁷, 21, F₉, 3, 34) (dual of [(21, 3), 26, 35]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9³⁷, 28, F₉, 3, 34) (dual of [(28, 3), 47, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,49P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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(3¹³⁸, 63, F₃, 3, 68) (dual of [(63, 3), 51, 69]-NRT-code)	[i]		OOA Duplication