# Design, decoding and optimized implementation of SECDED codes over GF(q)

## Abstract

A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selecting repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic.

- Inventors:

- Issue Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1134207

- Patent Number(s):
- 8,756,484

- Application Number:
- 14/029,379

- Assignee:
- Sandia Corporation( Albuquerque, NM); Micron Technology, Inc. (Boise, ID)

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Patent

- Resource Relation:
- Patent File Date: 2013 Sep 17

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Ward, H Lee, Ganti, Anand, and Resnick, David R.
```*Design, decoding and optimized implementation of SECDED codes over GF(q)*. United States: N. p., 2014.
Web.

```
Ward, H Lee, Ganti, Anand, & Resnick, David R.
```*Design, decoding and optimized implementation of SECDED codes over GF(q)*. United States.

```
Ward, H Lee, Ganti, Anand, and Resnick, David R. Tue .
"Design, decoding and optimized implementation of SECDED codes over GF(q)". United States. https://www.osti.gov/servlets/purl/1134207.
```

```
@article{osti_1134207,
```

title = {Design, decoding and optimized implementation of SECDED codes over GF(q)},

author = {Ward, H Lee and Ganti, Anand and Resnick, David R},

abstractNote = {A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selecting repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2014},

month = {6}

}

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LDPC Code Family for Millimeter-Wave Band Communications in a Wireless Network

patent-application, September 2012

- Abu-Surra, Shadi; Henige, Thomas M.; Pisek, Eran
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##
Error Correction Encoding Apparatus, Error Correction Decoding Apparatus, Nonvolatile Semiconductor Memory System, and Parity Check Matrix Generation Method

patent-application, February 2013

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- US Patent Application 13/406808; 20130055050