MinT - Information on Result #2247231

Information on Result #2247231

Linear OA(5¹⁴¹, 203, F₅, 64) (dual of [203, 62, 65]-code), using 1 times truncation based on linear OA(5¹⁴², 204, F₅, 65) (dual of [204, 62, 66]-code), using

concatenation of two codes [i] based on
1. linear OA(25³⁷, 68, F₂₅, 32) (dual of [68, 31, 33]-code), using
  - constructionÂ X applied to AG(F,32P) âŠ‚ AG(F,34P) [i] based on
    1. linear OA(25³⁶, 65, F₂₅, 32) (dual of [65, 29, 33]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]
    2. linear OA(25³⁴, 65, F₂₅, 30) (dual of [65, 31, 31]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
    3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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 OA(5¹⁴³, 205, F₅, 64) (dual of [205, 62, 65]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(5¹⁴⁴, 206, F₅, 64) (dual of [206, 62, 65]-code)	[i]	Code Embedding in Larger Space
3	Linear OOA(5¹⁴¹, 101, F₅, 2, 64) (dual of [(101, 2), 61, 65]-NRT-code)	[i]	OOA Folding