Editing Reed–Solomon error correction (section)

===Remarks===

Designers are not required to use the "natural" sizes of Reed–Solomon code blocks. A technique known as "shortening" can produce a smaller code of any desired size from a larger code. For example, the widely used (255,223) code can be converted to a (160,128) code by padding the unused portion of the source block with 95 binary zeroes and not transmitting them. At the decoder, the same portion of the block is loaded locally with binary zeroes.

The QR code, Ver 3 (29×29) uses interleaved blocks. The message has 26 data bytes and is encoded using two Reed-Solomon code blocks. Each block is a (255,233) Reed Solomon code shortened to a (35,13) code.

The Delsarte–Goethals–Seidel<ref>{{Citation |first1=Florian |last1=Pfender |first2=Günter M. |last2=Ziegler |title=Kissing Numbers, Sphere Packings, and Some Unexpected Proofs |journal=Notices of the American Mathematical Society |volume=51 |issue=8 |pages=873&ndash;883 |date=September 2004 |url=https://www.ams.org/notices/200408/fea-pfender.pdf |access-date=2009-09-28 |archive-date=2008-05-09 |archive-url = https://web.archive.org/web/20080509183217/http://www.ams.org/notices/200408/fea-pfender.pdf |url-status=live }}. Explains the Delsarte-Goethals-Seidel theorem as used in the context of the error correcting code for [[compact disc]].</ref> theorem illustrates an example of an application of shortened Reed–Solomon codes. In parallel to shortening, a technique known as [[Punctured code|puncturing]] allows omitting some of the encoded parity symbols.