Content deleted Content added
m Undid revision 1219004018 by 46.135.4.186 (talk) |
→Linear block codes: +link |
||
Line 132:
The theory of coding uses the ''N''-dimensional sphere model. For example, how many pennies can be packed into a circle on a tabletop, or in 3 dimensions, how many marbles can be packed into a globe. Other considerations enter the choice of a code. For example, hexagon packing into the constraint of a rectangular box will leave empty space at the corners. As the dimensions get larger, the percentage of empty space grows smaller. But at certain dimensions, the packing uses all the space and these codes are the so-called "perfect" codes. The only nontrivial and useful perfect codes are the distance-3 Hamming codes with parameters satisfying (2<sup>''r''</sup> – 1, 2<sup>''r''</sup> – 1 – ''r'', 3), and the [23,12,7] binary and [11,6,5] ternary Golay codes.<ref name=terras>
{{cite book | title = Fourier Analysis on Finite Groups and Applications |first=Audrey |last=Terras |author-link=Audrey Terras| publisher = [[Cambridge University Press]] | year = 1999 | isbn = 978-0-521-45718-7 | url = https://archive.org/details/fourieranalysiso0000terr | url-access = registration | page = [https://archive.org/details/fourieranalysiso0000terr/page/195 195] }}</ref><ref name=blahut>{{cite book |title = Algebraic Codes for Data Transmission |first=Richard E. |last=Blahut |author-link=Richard E. Blahut | publisher = Cambridge University Press | year = 2003 | isbn = 978-0-521-55374-2 | url = https://books.google.com/books?id=n0XHMY58tL8C&pg=PA60}}
</ref>
| |||