MinT - Information on Result #2490275

Information on Result #2490275

Linear OOA(3²³⁶, 298, F₃, 2, 63) (dual of [(298, 2), 360, 64]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²³⁴, 297, F₃, 2, 63) (dual of [(297, 2), 360, 64]-NRT-code), using

trace code [i] based on linear OOA(27⁷⁸, 99, F₂₇, 2, 63) (dual of [(99, 2), 120, 64]-NRT-code), using
- constructionÂ X applied to AG(2;F,126P) âŠ‚ AG(2;F,131P) [i] based on
  1. linear OOA(27⁷⁴, 95, F₂₇, 2, 63) (dual of [(95, 2), 116, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,126P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(27⁶⁹, 95, F₂₇, 2, 58) (dual of [(95, 2), 121, 59]-NRT-code), using algebraic-geometric NRT-code AG(2;F,131P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96 (see above)
  3. linear OOA(27⁴, 4, F₂₇, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27⁴, 27, F₂₇, 2, 4) (dual of [(27, 2), 50, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;50,27) [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(3²³⁶, 149, F₃, 4, 63) (dual of [(149, 4), 360, 64]-NRT-code)	[i]		OOA Folding