MinT - Information on Result #1048825

Information on Result #1048825

Linear OOA(8¹⁶⁴, 1030, F₈, 3, 50) (dual of [(1030, 3), 2926, 51]-NRT-code), using trace code based on linear OOA(64⁸², 515, F₆₄, 3, 50) (dual of [(515, 3), 1463, 51]-NRT-code), using

constructionÂ X applied to AG(3;F,1485P) âŠ‚ AG(3;F,1490P) [i] based on
1. linear OOA(64⁷⁸, 512, F₆₄, 3, 50) (dual of [(512, 3), 1458, 51]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1485P) [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(64⁷³, 512, F₆₄, 3, 45) (dual of [(512, 3), 1463, 46]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1490P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64⁴, 3, F₆₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;188,64) [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		Method
1	Linear OOA(8¹⁶⁴, 1030, F₈, 3, 49) (dual of [(1030, 3), 2926, 50]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(8¹⁶⁷, 1031, F₈, 3, 50) (dual of [(1031, 3), 2926, 51]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(8¹⁶⁵, 1030, F₈, 3, 50) (dual of [(1030, 3), 2925, 51]-NRT-code)	[i]	OOA Duplication