--- title: "Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes" url: https://daily.dev/posts/linear-feedback-shift-registers-for-the-uninitiated-part-xiv-gold-codes-ekqowcugq source_url: https://www.embeddedrelated.com/showarticle/1158.php type: article source: "EmbeddedRelated" published: 2026-05-31T07:47:58.168Z updated: 2026-05-31T09:19:09.768Z tags: ["python", "signal-processing"] reading_time: 60 upvotes: 0 comments: 0 language: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes **[EmbeddedRelated](https://daily.dev/sources/embeddedrelated)** · 60 min read · 0 upvotes · 0 comments ## Summary Gold codes solve the problem of multiple transmitters sharing spread-spectrum bandwidth without mutual interference. A single maximum-length PRBS fails when used across multiple transmitters because path delays, multipath, and asynchronous operation cause periodic phase alignment and high cross-correlation. Gold codes are constructed from 'preferred pairs' of m-sequences whose cross-correlation is bounded to a three-valued function with maximum amplitude of 2^((N/2)+1)+1, regardless of relative phase. The post derives the Three-Valued Cross-Correlation Theorem, shows how to find preferred polynomial pairs via decimation ratios, and demonstrates empirically in Python that up to 32767+2 distinct Gold sequences can be generated from a 15-bit LFSR pair. A working UART DSSS demo encodes 8 simultaneous messages using different Gold codes and decodes all of them with zero errors at a spreading ratio of 128. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: --- Tags: [#python](https://daily.dev/tags/python), [#signal-processing](https://daily.dev/tags/signal-processing) [View this post on daily.dev](https://daily.dev/posts/linear-feedback-shift-registers-for-the-uninitiated-part-xiv-gold-codes-ekqowcugq)