[tongwentao]

The Base64 codec is implemented and tested, but missing from the API reference. This adds it under Filter codecs, following the existing API-page layout. The class docstring now includes a small encoding/decoding example and describes the operation as encoding rather than compression.

Fixes #587.

Behavior and review notes

The new page makes an existing codec discoverable through the same API navigation as the other filters. The round-trip example demonstrates reversible Base64 encoding of binary data; it does not claim a reduction in size. The implementation, codec configuration, and encoded-byte compatibility are unchanged.

Validation:

• python -m pytest tests/test_base64.py src/numcodecs/base64.py -q --no-cov: 9 passed, including the new doctest.
• Pre-commit checks on all four changed files passed, including Ruff, repository review and mypy.
• Full Sphinx HTML build completed. It reports the same three warnings as an unmodified main documentation build in the same environment: the existing Blosc.decode_partial reference and two references in the Meson migration design document. No new warnings were introduced; a warnings-as-errors build therefore does not pass.
• Checked the generated Base64 page for the example and all documented method anchors, and verified the Filter codecs navigation link.
• The full test suite was not run; runtime behavior is unchanged.

Codex was used to prepare this documentation change and run the checks above.

TODO:

• Unit tests and/or doctests in docstrings
• Tests pass locally (focused Base64 tests and doctest)
• Docstrings and API docs for any new/modified user-facing classes and functions
• Changes documented in docs/release.md
• Docs build locally (three existing warnings, as noted above)
• GitHub Actions checks pass for ff95ea1 (39 successful, 2 publishing checks skipped; checked 2026-10-24).
• Codecov patch and project checks pass for the same commit; no runtime code added.