QR codes encode data using several error correction levels. Higher error correction allows for more damage or obstruction while still remaining readable, but requires more modules (the black and white squares). Uppercase letters, numbers, and some symbols use the alphanumeric mode, which is more efficient than the byte mode used for lowercase letters and other characters. Since alphanumeric mode requires fewer bits to encode the same information, a QR code with uppercase letters can achieve the same error correction level with fewer modules, making it smaller.
Researchers have demonstrated that antimony atoms implanted in silicon can function as qubits with impressive coherence times—a key factor for building practical quantum computers. Antimony's nuclear spin is less susceptible to noise from the surrounding silicon environment compared to electron spins typically used in silicon qubits, leading to these longer coherence times. This increased stability could simplify error correction procedures, making antimony-based qubits a promising candidate for scalable quantum computing. The demonstration used a scanning tunneling microscope to manipulate individual antimony atoms and measure their quantum properties, confirming their potential for high-fidelity quantum operations.
Hacker News users discuss the challenges of scaling quantum computing, particularly regarding error correction. Some express skepticism about the feasibility of building large, fault-tolerant quantum computers, citing the immense overhead required for error correction and the difficulty of maintaining coherence. Others are more optimistic, pointing to the steady progress being made and suggesting that specialized, error-resistant qubits like those based on antimony atoms could be a promising path forward. The discussion also touches upon the distinction between logical and physical qubits, with some emphasizing the importance of clearly communicating this difference to avoid hype and unrealistic expectations. A few commenters highlight the resource intensiveness of current error correction methods, noting that thousands of physical qubits might be needed for a single logical qubit, raising concerns about scalability.
This post details the process of creating a QR Code by hand, using the example of encoding "Hello, world!". It breaks down the procedure into several key steps: data analysis (determining the appropriate encoding mode and error correction level), data encoding (converting the text into a bit stream), error correction coding (adding redundancy for robustness), module placement in the matrix (populating the QR code grid with black and white modules based on the encoded data and fixed patterns), data masking (applying a mask pattern for optimal readability), and format and version information encoding (adding metadata about the QR Code's configuration). The post thoroughly explains each step, including the relevant algorithms and calculations, ultimately demonstrating how the final QR Code image is generated from the initial text string.
HN users largely praised the article for its clarity and detailed breakdown of QR code generation. Several appreciated the focus on the underlying principles and math, rather than just abstracting it away. One commenter pointed out the significance of explaining Reed-Solomon error correction, highlighting its crucial role in QR code functionality. Another user found the interactive demo particularly helpful for visualizing the process. Some discussion arose around alternative encoding schemes and their potential benefits, along with mention of a similar article focusing on PDF417 barcodes. A few commenters shared personal experiences using the article's information for practical projects.
Summary of Comments ( 73 )
https://news.ycombinator.com/item?id=43149077
Hacker News users discussed the trade-off between QR code size and error correction level. Several commenters pointed out that uppercase letters require less data than lowercase due to fewer bits needed in the alphanumeric mode. This smaller data size allows for a smaller QR code with the same error correction level or a higher error correction level for the same size. One commenter highlighted the importance of the QR code standard's details in understanding this phenomenon. Some also mentioned practical considerations, like the prevalence of uppercase URLs in certain contexts and the lack of visual difference in small QR codes. A few users suggested that the blog post's explanation was overly simplified, failing to fully explain the encoding mechanism and the impact of error correction. Finally, a commenter noted that different QR code generators may have varying implementations impacting resulting size.
The Hacker News post titled "Why are QR Codes with capital letters smaller than QR codes with lower case?" has generated several comments discussing the article's findings. The core idea discussed revolves around the alphanumeric encoding mode of QR codes being case-sensitive and how that affects the size of the resulting QR code.
Several commenters expand on the article's explanation regarding character encoding. They highlight that uppercase letters have a lower numeric value in the alphanumeric mode specification, resulting in fewer bits required to encode them. This efficiency in encoding translates to a smaller data payload, which in turn allows for a smaller QR code. One commenter explains that the savings comes from encoding two uppercase characters with 11 bits, whereas two lowercase characters require 11 bits each (22 total). Another points out the distinction between the encoding method and the size of the resulting graphic, emphasizing that encoding fewer bits leads to a smaller data matrix, which is then rendered visually as a smaller QR code.
Some commenters go deeper into the technical details of the alphanumeric mode. One commenter mentions how the article's example of encoding "HELLO" versus "hello" demonstrates this efficiency clearly. Another commenter provides further insight into the encoding specification, detailing the numeric values assigned to each alphanumeric character and how the encoding process concatenates and converts these values into binary data.
A few commenters offer practical perspectives on the issue. One points out that mixed-case encoding is almost always less efficient than all-uppercase or all-numeric encoding. Another highlights the importance of considering the target scanner and its ability to interpret different QR code sizes and complexities.
One commenter offers a related observation about micro QR codes and their limited error correction capability. Another suggests exploring alternative encoding schemes, like Base45, which can potentially offer better compression and smaller QR code sizes.
Finally, one commenter praises the article's clarity and conciseness, appreciating its effective explanation of a seemingly counter-intuitive phenomenon.