AI编程能力边界探索：基于 Claude Code 的 Spec Coding 项目实战｜得物技术

We present a new approach on low-rank matrix recovery (LRMR) based on Gabidulin Codes. Since most applications of LRMR deal with matrices over infinite fields, we use the recently introduced generalization of Gabidulin codes to fields of characterstic zero. We show that LRMR can be reduced to decoding of Gabidulin codes and discuss which field extensions can be used in the code construction.

Algorithms are presented that efficiently shape the parity bits of systematic irregular repeat-accumulate (IRA) low-density parity-check (LDPC) codes by following the sequential encoding order of the accumulator. Simulations over additive white Gaussian noise (AWGN) channels with on-off keying show a gain of up to 0.9 dB over uniform signaling.