MinT - Information on Result #2434362

Information on Result #2434362

Linear OOA(3¹⁸⁶, 108, F₃, 2, 108) (dual of [(108, 2), 30, 109]-NRT-code), using strength reduction based on linear OOA(3¹⁸⁶, 108, F₃, 2, 110) (dual of [(108, 2), 30, 111]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9³⁹, 27, F₉, 2, 36) (dual of [(27, 2), 15, 37]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9³⁹, 28, F₉, 2, 36) (dual of [(28, 2), 17, 37]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,19P) [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(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
  - extended Reedâ€“Solomon code RS_e(2,3) [i]
  - Hamming code H(2,3) [i]
  - Simplex code S(2,3) [i]
  - the Tetracode [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(3¹⁸⁶, 54, F₃, 4, 108) (dual of [(54, 4), 30, 109]-NRT-code)	[i]		OOA Folding