MinT - Information on Result #1048575

Information on Result #1048575

Linear OOA(4²⁵⁵, 1551, F₄, 3, 50) (dual of [(1551, 3), 4398, 51]-NRT-code), using trace code based on linear OOA(64⁸⁵, 517, F₆₄, 3, 50) (dual of [(517, 3), 1466, 51]-NRT-code), using

constructionÂ X applied to AG(3;F,1485P) âŠ‚ AG(3;F,1493P) [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(64⁷⁰, 512, F₆₄, 3, 42) (dual of [(512, 3), 1466, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1493P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64⁷, 5, F₆₄, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁷, 64, F₆₄, 3, 7) (dual of [(64, 3), 185, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;185,64) [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(4²⁵⁸, 1552, F₄, 3, 50) (dual of [(1552, 3), 4398, 51]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4²⁵⁶, 1551, F₄, 3, 50) (dual of [(1551, 3), 4397, 51]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4²⁵⁷, 1551, F₄, 3, 50) (dual of [(1551, 3), 4396, 51]-NRT-code)	[i]	OOA Duplication