MinT - Information on Result #2176134

Information on Result #2176134

Linear OA(2⁶⁷, 99, F₂, 22) (dual of [99, 32, 23]-code), using strength reduction based on linear OA(2⁶⁷, 99, F₂, 23) (dual of [99, 32, 24]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(2²⁴, 48, F₂, 11) (dual of [48, 24, 12]-code), using
  - extended quadratic residue code Q_e(48,2) [i]
2. linear OA(2⁴³, 51, F₂, 23) (dual of [51, 8, 24]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
      - projective code from ovoid in PG(3,Â 4) [i]
    2. 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.

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2⁶⁷, 33, F₂, 3, 22) (dual of [(33, 3), 32, 23]-NRT-code)	[i]		OOA Folding