MinT - Information on Result #661437

Information on Result #661437

Linear OA(2²¹⁹, 231, F₂, 105) (dual of [231, 12, 106]-code), using concatenation of two codes based on

linear OA(4⁷¹, 77, F₄, 52) (dual of [77, 6, 53]-code), using
- 3 times truncation [i] based on linear OA(4⁷⁴, 80, F₄, 55) (dual of [80, 6, 56]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16¹³, 16, F₁₆, 13) (dual of [16, 3, 14]-code or 16-arc in PG(12,16)), using
      - Reedâ€“Solomon code RS(3,16) [i]
    2. linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
      - extended Reedâ€“Solomon code RS_e(2,4) [i]
      - Simplex code S(2,4) [i]
linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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		This result only	Method
1	Linear OA(2²¹⁹, 231, F₂, 104) (dual of [231, 12, 105]-code)	[i]		Strength Reduction
2	Linear OOA(2²¹⁹, 33, F₂, 7, 105) (dual of [(33, 7), 12, 106]-NRT-code)	[i]		OOA Folding