MinT - Information on Result #2433691

Information on Result #2433691

Linear OOA(3¹⁷², 112, F₃, 2, 82) (dual of [(112, 2), 52, 83]-NRT-code), using strength reduction based on linear OOA(3¹⁷², 112, F₃, 2, 83) (dual of [(112, 2), 52, 84]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9³⁰, 28, F₉, 2, 27) (dual of [(28, 2), 26, 28]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,28P) [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(3¹⁷¹, 111, F₃, 2, 81) (dual of [(111, 2), 51, 82]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(3¹⁷², 56, F₃, 4, 82) (dual of [(56, 4), 52, 83]-NRT-code)	[i]		OOA Folding