MinT - Information on Result #2434768

Information on Result #2434768

Linear OOA(3¹⁹⁴, 126, F₃, 2, 88) (dual of [(126, 2), 58, 89]-NRT-code), using strength reduction based on linear OOA(3¹⁹⁴, 126, F₃, 2, 89) (dual of [(126, 2), 58, 90]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁵⁵, 42, F₉, 2, 44) (dual of [(42, 2), 29, 45]-NRT-code), using
  - constructionÂ X applied to AG(2;F,33P) âŠ‚ AG(2;F,37P) [i] based on
    1. linear OOA(9⁵², 39, F₉, 2, 44) (dual of [(39, 2), 26, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,33P) [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]
    2. linear OOA(9⁴⁸, 39, F₉, 2, 40) (dual of [(39, 2), 30, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,37P) [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40 (see above)
    3. linear OOA(9³, 3, F₉, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(9³, 9, F₉, 2, 3) (dual of [(9, 2), 15, 4]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;15,9) [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(3¹⁹⁴, 63, F₃, 4, 88) (dual of [(63, 4), 58, 89]-NRT-code)	[i]		OOA Folding