MinT - Information on Result #2765339

Information on Result #2765339

Linear OOA(2²¹⁵, 60, F₂, 4, 126) (dual of [(60, 4), 25, 127]-NRT-code), using strength reduction based on linear OOA(2²¹⁵, 60, F₂, 4, 127) (dual of [(60, 4), 25, 128]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁵, 20, F₃₂, 15) (dual of [20, 5, 16]-code or 20-arc in PG(14,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁵, 32, F₃₂, 15) (dual of [32, 17, 16]-code or 32-arc in PG(14,32)), using
    - Reedâ€“Solomon code RS(17,32) [i]
2. linear OOA(2⁷, 3, F₂, 4, 7) (dual of [(3, 4), 5, 8]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;5,2) [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		Method
1	Linear OOA(2²¹⁶, 60, F₂, 4, 126) (dual of [(60, 4), 24, 127]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²¹⁷, 60, F₂, 4, 126) (dual of [(60, 4), 23, 127]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²¹⁴, 59, F₂, 4, 125) (dual of [(59, 4), 22, 126]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²¹³, 59, F₂, 4, 124) (dual of [(59, 4), 23, 125]-NRT-code)	[i]
5	Linear OOA(2²¹², 59, F₂, 4, 123) (dual of [(59, 4), 24, 124]-NRT-code)	[i]
6	Linear OOA(2²¹¹, 59, F₂, 4, 122) (dual of [(59, 4), 25, 123]-NRT-code)	[i]
7	Linear OOA(2²¹⁰, 58, F₂, 4, 121) (dual of [(58, 4), 22, 122]-NRT-code)	[i]
8	Linear OOA(2²⁰⁹, 58, F₂, 4, 120) (dual of [(58, 4), 23, 121]-NRT-code)	[i]
9	Linear OOA(2²⁰⁸, 58, F₂, 4, 119) (dual of [(58, 4), 24, 120]-NRT-code)	[i]
10	Linear OOA(2²⁰⁷, 58, F₂, 4, 118) (dual of [(58, 4), 25, 119]-NRT-code)	[i]
11	Linear OOA(2²⁰⁶, 57, F₂, 4, 117) (dual of [(57, 4), 22, 118]-NRT-code)	[i]
12	Linear OOA(2²⁰⁵, 57, F₂, 4, 116) (dual of [(57, 4), 23, 117]-NRT-code)	[i]
13	Linear OOA(2²¹⁵, 30, F₂, 8, 126) (dual of [(30, 8), 25, 127]-NRT-code)	[i]	OOA Folding