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- T. Aaron Gulliver, Jon-Lark Kim, Yoonjin Lee
- IEEE Transactions on Information Theory
- 2008

We construct new MDS or near-MDS self-dual codes over large finite fields. In particular, we show that there exists a Euclidean self-dual MDS code of length n = q over GF(q) whenever q = 2<sup>m</sup> (m ges 2) using a Reed-Solomon (RS) code and its extension. It turns out that this multiple description source (MDS) self-dual code is an extended duadic… (More)

- Steven T. Dougherty, Jon-Lark Kim, Hamid Kulosman
- Des. Codes Cryptography
- 2009

The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(p e , l) (including Z p e). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite… (More)

- T. Aaron Gulliver, Jon-Lark Kim
- IEEE Transactions on Information Theory
- 2004

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 extremal additive circulant self-dual codes of lengths up to 15, and construct good codes for lengths… (More)

- Jon-Lark Kim
- IEEE Trans. Information Theory
- 2001

- Steven T. Dougherty, Jon-Lark Kim, Patrick Solé
- Adv. in Math. of Comm.
- 2007

Two class association schemes consist of either strongly regular graphs (SRG) or doubly regular tournaments (DRT). We construct self-dual codes from the adjacency matrices of these schemes. This generalizes the construction of Pless ternary Symmetry codes, Karlin binary Double Circulant codes, Calderbank and Sloane quaternary double circulant codes, and… (More)

LDPC codes are serious contenders to Turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m ≥ 2, Lazeb-nik and Ustimenko construct a q-regular bipartite graph D(m, q) on 2q m vertices, which has girth at least 2m/2 + 4. We regard… (More)

- Jon-Lark Kim, Vera Pless
- Finite Fields and Their Applications
- 2007

A binary code with the same weight distribution as its dual code is called formally self-dual (f.s.d.). We only consider f.s.d. even codes (codes with only even weight codewords). We show that any formally self-dual even binary code C of length n not divisible by 8 is balanced. We show that the weight distribution of a balanced near-extremal f.s.d. even… (More)

- Jon-Lark Kim, Uri N. Peled, I. Perepelitsa, Vera Pless, Shmuel Friedland
- IEEE Transactions on Information Theory
- 2004

Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which… (More)

- Jon-Lark Kim, Yoonjin Lee
- J. Comb. Theory, Ser. A
- 2004

- Steven T. Dougherty, Jon-Lark Kim, Hamid Kulosman, Hongwei Liu
- Finite Fields and Their Applications
- 2010

We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We… (More)