MinT - Information on Result #939569

Information on Result #939569

Linear OOA(4¹⁵⁶, 537, F₄, 2, 42) (dual of [(537, 2), 918, 43]-NRT-code), using trace code based on linear OOA(64⁵², 179, F₆₄, 2, 42) (dual of [(179, 2), 306, 43]-NRT-code), using

constructionÂ X applied to AG(2;F,309P) âŠ‚ AG(2;F,313P) [i] based on
1. linear OOA(64⁴⁹, 176, F₆₄, 2, 42) (dual of [(176, 2), 303, 43]-NRT-code), using algebraic-geometric NRT-code AG(2;F,309P) [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(64⁴⁵, 176, F₆₄, 2, 38) (dual of [(176, 2), 307, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,313P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64³, 3, F₆₄, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64³, 64, F₆₄, 2, 3) (dual of [(64, 2), 125, 4]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;125,64) [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(4¹⁵⁸, 538, F₄, 2, 42) (dual of [(538, 2), 918, 43]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁵⁷, 537, F₄, 2, 42) (dual of [(537, 2), 917, 43]-NRT-code)	[i]		OOA Duplication