MinT - Information on Result #1703450

Information on Result #1703450

Linear OOA(2²¹⁶, 299597, F₂, 8, 21) (dual of [(299597, 8), 2396560, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁶, 299597, F₂, 7, 21) (dual of [(299597, 7), 2096963, 22]-NRT-code), using

OOA 7-folding [i] based on linear OA(2²¹⁶, 2097179, F₂, 21) (dual of [2097179, 2096963, 22]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2²¹², 2097175, F₂, 21) (dual of [2097175, 2096963, 22]-code), using
  - constructionÂ X4 applied to C_e(20) âŠ‚ C_e(18) [i] based on
    1. linear OA(2²¹¹, 2097152, F₂, 21) (dual of [2097152, 2096941, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(2¹⁹⁰, 2097152, F₂, 19) (dual of [2097152, 2096962, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(2²², 23, F₂, 21) (dual of [23, 1, 22]-code), using
      - strength reduction [i] based on linear OA(2²², 23, F₂, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
        dual of repetition code with length 23 [i]
    4. linear OA(2¹, 23, F₂, 1) (dual of [23, 22, 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: 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(2²¹⁷, 299597, F₂, 8, 21) (dual of [(299597, 8), 2396559, 22]-NRT-code)	[i]		OOA Duplication