MinT - Information on Result #940717

Information on Result #940717

Linear OOA(8¹⁶⁸, 376, F₈, 2, 65) (dual of [(376, 2), 584, 66]-NRT-code), using trace code based on linear OOA(64⁸⁴, 188, F₆₄, 2, 65) (dual of [(188, 2), 292, 66]-NRT-code), using

constructionÂ X applied to AG(2;F,286P) âŠ‚ AG(2;F,299P) [i] based on
1. linear OOA(64⁷², 176, F₆₄, 2, 65) (dual of [(176, 2), 280, 66]-NRT-code), using algebraic-geometric NRT-code AG(2;F,286P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(64⁵⁹, 176, F₆₄, 2, 52) (dual of [(176, 2), 293, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,299P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹², 12, F₆₄, 2, 12) (dual of [(12, 2), 12, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹², 64, F₆₄, 2, 12) (dual of [(64, 2), 116, 13]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;116,64) [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(8¹⁶⁹, 376, F₈, 2, 65) (dual of [(376, 2), 583, 66]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(8¹⁶⁸, 188, F₈, 3, 65) (dual of [(188, 3), 396, 66]-NRT-code)	[i]		OOA Folding