MinT - Information on Result #661474

Information on Result #661474

Linear OA(2²⁴³, 335, F₂, 75) (dual of [335, 92, 76]-code), using concatenation of two codes based on

linear OA(16⁴⁴, 67, F₁₆, 37) (dual of [67, 23, 38]-code), using
- constructionÂ X applied to AG(F,26P) âŠ‚ AG(F,28P) [i] based on
  1. linear OA(16⁴³, 64, F₁₆, 37) (dual of [64, 21, 38]-code), using algebraic-geometric code AG(F,26P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
  2. linear OA(16⁴¹, 64, F₁₆, 35) (dual of [64, 23, 36]-code), using algebraic-geometric code AG(F,28P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(2²⁴³, 335, F₂, 74) (dual of [335, 92, 75]-code)	[i]	Strength Reduction
2	Linear OA(2²⁴⁴, 336, F₂, 75) (dual of [336, 92, 76]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²⁴⁵, 337, F₂, 75) (dual of [337, 92, 76]-code)	[i]
4	Linear OA(2²⁴⁶, 338, F₂, 75) (dual of [338, 92, 76]-code)	[i]
5	Linear OA(2²⁴⁷, 339, F₂, 75) (dual of [339, 92, 76]-code)	[i]
6	Linear OA(2²⁴⁸, 340, F₂, 75) (dual of [340, 92, 76]-code)	[i]
7	Linear OA(2²⁴², 334, F₂, 74) (dual of [334, 92, 75]-code)	[i]	Truncation
8	Linear OOA(2²⁴³, 167, F₂, 2, 75) (dual of [(167, 2), 91, 76]-NRT-code)	[i]	OOA Folding
9	Linear OOA(2²⁴³, 111, F₂, 3, 75) (dual of [(111, 3), 90, 76]-NRT-code)	[i]	OOA Folding