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s-Extremal Additive Codes over GF(4)
2006 Edition, July 1, 2006 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality...

Circulant based extremal additive self-dual codes over GF(4)
2004 Edition, Volume 50, February 1, 2004 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

It is well known that the problem of finding stabilizer quantum-error-correcting codes (QECC) is transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Our purpose is to classify the...

Weight hierarchies of extremal non-chain ternary codes of dimension 4
2001 Edition, January 1, 2001 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d/sub 1/,d/sub 2/,...,d/sub k/) where d/sub r/ is the smallest support of an r-dimensional subcode of C. An [n,k;q] code is extremal non-chain if for any r and s, where 1/spl...

Weight hierarchies of extremal non-chain binary codes of dimension 4
1999 Edition, Volume 45, January 1, 1999 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d/sub 1/,d/sub 2/,/spl middot//spl middot//spl middot/,d/sub k/) where d/sub r/ is the smallest support of an r-dimensional subcode of C. An [n,k;q] code is extremal nonchain if, for any r...

Upper Bounds for the Lengths of $s$ -Extremal Codes Over $\BBF _{2}$ , $\BBF _{4}$ , and $\BBF _{2} + u\BBF _{2}$
2008 Edition, Volume 54, January 1, 2008 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Our purpose is to find an upper bound for the length of an s-extremal code over F2 (resp. F4) when d equiv 2 (mod 4) (resp. d odd). This question is left open in [A bound for certain s -extremal lattices and codes, Archiv der Mathematik, vol....

New good Hermitian self-dual codes over GF(4)
2001 Edition, January 1, 2001 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

The purpose of this paper is to construct new Hermitian self-dual codes over GF(4) of lengths 22, 24, 26, and 32 which have the highest known minimum weights. In particular, for length 22, we construct 8 new extremal self-dual [22,11,8] codes over...

Quantum stabilizer codes construction from Hermitian self-orthogonal codes over GF(4)
2018 Edition, Volume 20, June 1, 2018 - Editorial Department of Journal of Communications and Networks

In order to construct quantum error correction code, we consider additive codes over Galois field GF(4), which are self-orthogonal with respect to a certain Hermitian product. In this paper, we first propose a new approach to the construction of Hermitian...

On the classification of self-dual additive codes over GF(9)
2010 Edition, June 1, 2010 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have previously been classified up to length 8. In this paper, all codes of length 9 and 10 are classified, using a new algorithm that combines two graph representations...

Quantum error correction via codes over GF(4)
1998 Edition, Volume 44, July 1, 1998 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

The problem of finding quantum error correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented,...

Quantum error correction via codes over GF(2)
2009 Edition, June 1, 2009 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

It is well known that n-length stabilizer quantum error correcting codes (QECCs) can be obtained via n-length classical error correction codes (CECCs) over GF(4), that are additive and self-orthogonal with respect to the trace Hermitian inner product. But,...

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