ISSN:
1573-7586
Keywords:
Z 4-linear codes
;
Goethals code
;
Delsarte-Goethals code
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract The Goethals code is a binary nonlinear code of length 2 m+1 which has % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIYaWaaW% baaSqabeaacaaIYaWaaWbaaWqabeaacaWGTbGaey4kaSIaaGymaaaa% aaGccqGHsislcaaIZaGaamyBaiabgkHiTiaaikdaaaa!41EE!\[2^{2^{m + 1} } - 3m - 2\] codewords and minimum Hamming distance 8 for any odd m 〉- 3. Recently, Hammons et. al. showed that codes with the same weight distribution can be obtained via the Gray map from a linear code over Z 4 of length 2 m and Lee distance 8. The Gray map of the dual of the corresponding Z 4 code is a Delsarte-Goethals code. We construct codes over Z 4 such that their Gray maps lead to codes with the same weight distribution as the Goethals codes and the Delsarte-Goethals codes.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00129768
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