MinT - Information on Result #1130475

Information on Result #1130475

Linear OOA(2⁹⁹, 104862, F₂, 6, 11) (dual of [(104862, 6), 629073, 12]-NRT-code), using OOA 5-folding and stacking with additional row based on linear OA(2⁹⁹, 524311, F₂, 11) (dual of [524311, 524212, 12]-code), using

2 times code embedding in larger space [i] based on linear OA(2⁹⁷, 524309, F₂, 11) (dual of [524309, 524212, 12]-code), using
- constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
  1. linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(2⁷⁷, 524288, F₂, 9) (dual of [524288, 524211, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  3. linear OA(2²⁰, 21, F₂, 19) (dual of [21, 1, 20]-code), using
    - strength reduction [i] based on linear OA(2²⁰, 21, F₂, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
      - dual of repetition code with length 21 [i]
  4. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2⁹⁹, 104862, F₂, 6, 10) (dual of [(104862, 6), 629073, 11]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁰⁰, 104862, F₂, 6, 11) (dual of [(104862, 6), 629072, 12]-NRT-code)	[i]		OOA Duplication