New Lower Bounds on Binary Constant Weight Error-Correcting Codes

Let \( A(n, d, w) \) denote the maximum size of a binary code with length \( n \), minimum distance \( d \), and constant weight \( w \). The following lower bounds are here obtained in computer searches for codes with prescribed automorphisms: \( A(16, 4, 6) \geq 624 \), \( A(19, 4, 8) \geq 4698 \), \( A(20, 4, 8) \geq 7830 \), \( A(21, 4, 6) \geq 2880 \), \( A(22, 6, 6) \geq 343 \), \( A(24, 4, 5) \geq 1920 \), \( A(24, 6, 9) \geq 3080 \), \( A(24, 6, 11) \geq 5376 \), \( A(24, 6, 12) \geq 5558 \), \( A(25, 4, 5) \geq 2380 \), \( A(25, 6, 10) \geq 6600 \), \( A(26, 4, 5) \geq 2816 \), and \( A(27, 4, 5) \geq 3456 \).