New Upper Bounds on Binary Linear Codes and a -Code With a Better-Than-Linear Gray Image

Using integer linear programming and table-lookups, we prove that there is no binary linear [1988, 12, 992] code. As a by-product, the non-existence of binary linear codes with the parameters [324, 10, 160], [356, 10, 176], [772, 11, 384], and [836, 11, 416] is shown. Our work is motivated by the re...

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Veröffentlicht in:IEEE transactions on information theory Jg. 62; H. 12; S. 6768 - 6771
Hauptverfasser: Kiermaier, Michael, Wassermann, Alfred, Zwanzger, Johannes
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.12.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Information theory
Integer linear programming
Integer programming
Kerdock codes
Linear codes
Linear programming
ring-linear codes
Table lookup
Two dimensional displays
Upper bound
Zinc
ISSN:0018-9448, 1557-9654
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Zusammenfassung:Using integer linear programming and table-lookups, we prove that there is no binary linear [1988, 12, 992] code. As a by-product, the non-existence of binary linear codes with the parameters [324, 10, 160], [356, 10, 176], [772, 11, 384], and [836, 11, 416] is shown. Our work is motivated by the recent construction of the extended dualized Kerdock code K 6 *, which is a Z 4 -linear code having a non-linear binary Gray image with the parameters 1988, 2 12 ,992. By our result, the code K 6 * can be added to the small list of Z 4 -codes for which it is known that the Gray image is better than any binary linear code.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2016.2612654