MinT - Information on Result #2295760

Information on Result #2295760

Linear OA(2²²², 272, F₂, 77) (dual of [272, 50, 78]-code), using adding a parity check bit based on linear OA(2²²¹, 271, F₂, 76) (dual of [271, 50, 77]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(2²⁰⁰, 247, F₂, 76) (dual of [247, 47, 77]-code), using
  - 9 times truncation [i] based on linear OA(2²⁰⁹, 256, F₂, 85) (dual of [256, 47, 86]-code), using
    - an extension C_e(84) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,84], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 85 [i]
2. linear OA(2²⁰⁰, 250, F₂, 64) (dual of [250, 50, 65]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²⁰⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 1 276078 301342 703888 154877 366880 741846 289906 449506 221104 908560 [i]
3. linear OA(2¹⁸, 21, F₂, 11) (dual of [21, 3, 12]-code), using
  - repeating each code word 3 times [i] based on linear OA(2⁴, 7, F₂, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), using
    - Simplex code S(3,2) [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		Method
1	Linear OA(2²²², 272, F₂, 76) (dual of [272, 50, 77]-code)	[i]	Strength Reduction
2	Linear OA(2²²³, 273, F₂, 77) (dual of [273, 50, 78]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²²⁴, 274, F₂, 77) (dual of [274, 50, 78]-code)	[i]	Code Embedding in Larger Space