MinT - Information on Result #940669

Information on Result #940669

Linear OOA(8¹⁶⁴, 1034, F₈, 2, 49) (dual of [(1034, 2), 1904, 50]-NRT-code), using trace code based on linear OOA(64⁸², 517, F₆₄, 2, 49) (dual of [(517, 2), 952, 50]-NRT-code), using

constructionÂ X applied to AG(2;F,974P) âŠ‚ AG(2;F,980P) [i] based on
1. linear OOA(64⁷⁷, 512, F₆₄, 2, 49) (dual of [(512, 2), 947, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,974P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
  - the Hermitian function field over F₆₄ [i]
2. linear OOA(64⁷¹, 512, F₆₄, 2, 43) (dual of [(512, 2), 953, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,980P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64⁵, 5, F₆₄, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁵, 64, F₆₄, 2, 5) (dual of [(64, 2), 123, 6]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;123,64) [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(8¹⁶⁵, 1034, F₈, 2, 49) (dual of [(1034, 2), 1903, 50]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(8¹⁶⁴, 517, F₈, 3, 49) (dual of [(517, 3), 1387, 50]-NRT-code)	[i]		OOA Folding