On this page, a list of known 'short' multiple write binary WOM codes is composed. Only individual code instances are included, no constructions containing free parameters. Main reason for creation was to have some way to get an overview which codes have been found, how they are defined and how they compare to other codes.
| Length | Symbols per write | Rfixed | Rsum | Comment | Code |
|---|
| 3 | 4,3,2 | 1 | 1.52832 | Yaakobi et al. - 'Codes for Write-Once Memories' - 2012 | |
| 4 | 5,7,2 | 0.75 | 1.53232 | Added 2017-05-09 (known write number) | Pattern sets |
| 5 | 5,5,5 | 1.39316 | 1.39316 | Klarner - reported by Rivest&Shamir in 1982 | |
| 5 | 6,5,6 | 1.39316 | 1.49837 | | Symbol mapping (25 data points) |
| 5 | 6,9,4 | 1.2 | 1.55098 | Added 2017-05-09 (known write number) | Pattern sets |
| 6 | 7,12,8 | 1.40368 | 1.56539 | | Symbol mapping (26 data points) |
| 6 | 7,14,8 | 1.40368 | 1.60245 | Added 2017-05-09 (known write number) | Pattern sets |
| 7 | 8,8,8 | 1.28571 | 1.28571 | Rivest&Shamir - 'How to reuse a Write-Once Memory' - 1982 | |
| 7 | 8,8,8 | 1.28571 | 1.28571 | Cohen et al. - 'Linear binary code for write-once memories' - 1986 | |
| 7 | 8,15,15 | 1.28571 | 1.54483 | | Symbol mapping (27 data points) |
| 7 | 27,13,8 | 1.28571 | 1.63648 | Added 2017-05-09 (known write number) | Pattern sets |
| 8 | 16,16,16 | 1.5 | 1.5 | | Symbol mapping (28 data points) |
| 8 | 20,15,15 | 1.46508 | 1.51696 | | Symbol mapping (28 data points |
| 8 | 37,17,16 | 1.5 | 1.66211 | Added 2017-05-09 (known write number) | Pattern sets |
| 9 | 24,24,24 | 1.52832 | 1.52832 | | Symbol mapping (29 data points |
| 10 | 36,36,36 | 1.55098 | 1.55098 | | Symbol mapping (210 data points |
| 11 | 64,64,64 | 1.63636 | 1.63636 | | Symbol mapping (211 data points |
| 11 | 67,68,64 | 1.63636 | 1.65032 | | Symbol mapping (211 data points |
| 12 | 65,81,64 | 1.5 | 1.53018 | Saxe - reported by Rivest&Shamir in 1982 | |
| 12 | 72,160,64 | 1.5 | 1.62432 | | Symbol mapping (212 data points) |
| 12 | 75,75,75 | 1.55720 | 1.55720 | | Symbol mapping (212 data points) |
| 16 | 29,29,29 | 1.6875 | 1.6875 | Added 2017-04-24. Known write number assumed.
First two writes use an arbitrary map, last write a parity check matrix. | C++ demo program (including code definition) |
| 23 | 211,211,211 | 1.43478 | 1.43478 | Cohen et al. - 'Linear binary code for write-once memories' - 1986 | |
| Length | Symbols per write | Rfixed | Rsum | Comment | Code |
|---|
| 4 | 5,3,3,2 | 1 | 1.62296 | Added 2017-05-09 (known write number) | Pattern sets |
| 5 | 6,5,3,4 | 1.26797 | 1.69837 | Added 2017-05-09 (known write number) | Pattern sets |
| 6 | 7,5,10,4 | 1.33333 | 1.74187 | Added 2017-05-09 (known write number) | Pattern sets |
| 7 | 7,7,7,7 | 1.60420 | 1.60420 | D. Leavitt - reported by Rivest&Shamir in 1982 | |
| 7 | 8,7,8,8 | 1.60420 | 1.68676 | Merkx - 'Womcodes constructed with projective geometries' - 1984 | |
| 7 | 8,7,11,8 | 1.60420 | 1.75240 | Merkx - 'Womcodes constructed with projective geometries' - 1984 | |
| 7 | 8,7,12,8 | 1.6042 | 1.77033 | Added 2017-05-09 (known write number) | Pattern sets |
| 8 | 8,14,11,8 | 1.5 | 1.65835 | Merkx - 'Womcodes constructed with projective geometries' - 1984 | |
| 8 | 9,29,10,8 | 1.5 | 1.79373 | Added 2017-05-09 (known write number) | Pattern sets |
| 9 | 10,14,14,14 | 1.47641 | 1.63822 | | Symbol mapping (29 data points) |
| 10 | 24,24,24,24 | 1.6 | 1.6 | | Symbol mapping (210 data points) |
| 12 | 25,25,25,25 | 1.66667 | 1.66667 | | Symbol mapping (212 data points) |
| 14 | 26,26,26,26 | 1.71429 | 1.71429 | | Symbol mapping (214 data points) |
| 16 | 27,27,27,27 | 1.75 | 1.75 | | Symbol mapping (216 data points) |
| 18 | 28,28,28,28 | 1.77778 | 1.77778 | Added 2017-04-18 | Symbol mapping (218 data points) |