# On Weight Distributions of Shifts of Goethals-like Codes

On Weight Distributions of Shifts of Goethals-like Codes We study weight distributions of shifts of codes from a well-known family: the 3-error-correcting binary nonlinear Goethals-like codes of length n = 2 m , where m ≥ 6 is even. These codes have covering radius ρ = 6. We know the weight distribution of any shift of weight i = 1, 2, 3, 5, or 6. For a shift of weight 4, the weight distribution is uniquely defined by the number of leaders in this shift, i.e., the number of vectors of weight 4. We also consider the weight distribution of shifts of codes with minimum distance 7 obtained by deleting any one position of a Goethals-like code of length n. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# On Weight Distributions of Shifts of Goethals-like Codes

, Volume 40 (2) – Dec 16, 2004
17 pages

/lp/springer_journal/on-weight-distributions-of-shifts-of-goethals-like-codes-l90o5RsqvD
Publisher
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/B:PRIT.0000043926.60991.7e
Publisher site
See Article on Publisher Site

### Abstract

We study weight distributions of shifts of codes from a well-known family: the 3-error-correcting binary nonlinear Goethals-like codes of length n = 2 m , where m ≥ 6 is even. These codes have covering radius ρ = 6. We know the weight distribution of any shift of weight i = 1, 2, 3, 5, or 6. For a shift of weight 4, the weight distribution is uniquely defined by the number of leaders in this shift, i.e., the number of vectors of weight 4. We also consider the weight distribution of shifts of codes with minimum distance 7 obtained by deleting any one position of a Goethals-like code of length n.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Dec 16, 2004

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations